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On the structure of finitely presented Bestvina–Brady groups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2024-03-07 Priyavrat Deshpande, Mallika Roy
Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups using finite simplicial graphs. The isomorphism type of the group is uniquely determined by the graph. Moreover, many structural properties of right-angled Artin groups can be expressed in terms of their defining graph. In
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The omega-reducibility of pseudovarieties of ordered monoids representing low levels of concatenation hierarchies Int. J. Algebra Comput. (IF 0.8) Pub Date : 2024-03-07 Jana Volaříková
We deal with the question of the ω-reducibility of pseudovarieties of ordered monoids corresponding to levels of concatenation hierarchies of regular languages. A pseudovariety of ordered monoids V is called ω-reducible if, given a finite ordered monoid M, for every inequality of pseudowords that is valid in V, there exists an inequality of ω-words that is also valid in V and has the same “imprint”
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On computing the closures of solvable permutation groups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2024-03-07 Ilia Ponomarenko, Andrey V. Vasil’ev
Let m≥3 be an integer. It is proved that the m-closure of a given solvable permutation group of degree n can be constructed in time nO(m).
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Dehornoy’s class and Sylows for set-theoretical solutions of the Yang–Baxter equation Int. J. Algebra Comput. (IF 0.8) Pub Date : 2024-03-07 Edouard Feingesicht
We explain how the germ of the structure group of a cycle set decomposes as a product of its Sylow-subgroups, and how this process can be reversed to construct cycle sets from ones with coprime classes. We study Dehornoy’s class associated to a cycle set, and conjecture a bound that we prove in a specific case. We combine the use of braces and a monomial representation, in particular to answer a question
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Commuting and product-zero probability in finite rings Int. J. Algebra Comput. (IF 0.8) Pub Date : 2024-02-20 Pavel Shumyatsky, Matteo Vannacci
Let cp(R) be the probability that two random elements of a finite ring R commute and zp(R) the probability that the product of two random elements in R is zero. We show that if cp(R)=𝜀, then there exists a Lie-ideal D in the Lie-ring (R,[⋅,⋅]) with 𝜀-bounded index and with [D,D] of 𝜀-bounded order. If zp(R)=𝜀, then there exists an ideal D in R with 𝜀-bounded index and D2 of 𝜀-bounded order. These
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Subpolygroup commutativity degree of finite extension polygroup Int. J. Algebra Comput. (IF 0.8) Pub Date : 2024-01-19 M. Al-Tahan, B. Davvaz, P. Harikrishnan, P. Pallavi
In this paper, we consider finite extension polygroups as a special class of polygroups to study probabilistic polygroup theory. In this regard, we study the subpolygroup lattice of the extension polygroups. By using the results of the subpolygroup lattice, we obtain an explicit formula for the subpolygroup commutativity degree of the extension polygroup.
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Detecting similarities of rational plane curves using complex differential invariants Int. J. Algebra Comput. (IF 0.8) Pub Date : 2024-01-10 Hüsnü Anıl Çoban
We present a new and efficient method to detect whether or not two given rational plane curves are similar. If both curves are the same, the method finds the symmetries of the curve. The method relies on the introduction of a complex differential invariant that has a nice behavior with respect to Möbius transformations, which are the mappings lying behind the similarities in the parameter space. From
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A census of small Schurian association schemes Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-12-29 Jesse Lansdown
Using the classification of transitive groups of degree n, for 2≤n≤48, we classify the Schurian association schemes of order n, and as a consequence, the transitive groups of degree n that are 2-closed. In addition, we compute the character table of each association scheme and provide a census of important properties. Finally, we compute the 2-closure of each transitive group of degree n, for 2≤n≤48
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Symmetric polynomials in free center-by-metabelian Lie algebras of rank 2 Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-12-20 C. E. Kofinas
Let C2 be the free center-by-metabelian Lie algebra of rank 2 freely generated by the set {x1,x2}. Let PC2 be the Lie subalgebra of symmetric polynomials in C2, that is, PC2 consists of all the elements f(x1,x2) in C2 such that f(x1,x2)=f(x2,x1). We give a linear basis and a minimal infinite generating set for PC2, thus extending results of Ş. Findik and N. Ögüşlü [Palindromes in the free metabelian
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Quadratic equations in metabelian Baumslag–Solitar groups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-08-21 Richard Mandel, Alexander Ushakov
For a finitely generated group G, the Diophantine problem over G is the algorithmic problem of deciding whether a given equation W(z1,z2,…,zk)=1 (perhaps restricted to a fixed subclass of equations) has a solution in G. In this paper, we investigate the algorithmic complexity of the Diophantine problem for the class 𝒞 of quadratic equations over the metabelian Baumslag–Solitar groups BS(1,n). We prove
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Differentially fixed ideals in affine semigroup rings Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-08-17 Lance Edward Miller, William D. Taylor, Janet Vassilev
We give a complete characterization of when monomial ideals are fixed by differential operators of affine semigroup rings over ℂ. Perhaps surprisingly, every monomial ideal is fixed by an infinite set of homogeneous differential operators and is in fact determined by them. This opens up a new tool for studying monomial ideals. We explore applications of this to (mixed) multiplier ideals and other variants
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On the number of countable subdirect powers of unary algebras Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-08-12 Nik Ruškuc, Bill de Witt
A finite unary algebra (A,F) has only countably many countable subdirect powers if and only if every operation f∈F is either a permutation or a constant mapping.
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Acylindricity of the action of right-angled Artin groups on extension graphs Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-08-07 Eon-Kyung Lee, Sang-Jin Lee
The action of a right-angled Artin group on its extension graph is known to be acylindrical because the cardinality of the so-called r-quasi-stabilizer of a pair of distant points is bounded above by a function of r. The known upper bound of the cardinality is an exponential function of r. In this paper we show that the r-quasi-stabilizer is a subset of a cyclic group and its cardinality is bounded
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Group-like small cancellation theory for rings Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-08-03 A. Atkarskaya, A. Kanel-Belov, E. Plotkin, E. Rips
In this paper, we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relations. We show that the obtained ring is non-trivial. Moreover, we show that this ring enjoys a global filtration that agrees with relations, find a basis of the
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On amenability and measure of maximal entropy for semigroups of rational maps: II Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-29 Carlos Cabrera, Peter Makienko
We compare dynamical and algebraic properties of semigroups of rational maps. In particular, we show a version of the Day-von Neumann conjecture and give a partial positive answer to “Sushkievich’s problem” for semigroups of rational maps. We relate these conjectures with Furstenberg’s ×2×3 problem and prove a coarse version of Furstenberg’s problem for semigroups of non-exceptional polynomials.
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On k-geodetic graphs and groups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-28 Murray Elder, Adam Piggott, Kane Townsend
We call a graph k-geodetic, for some k≥1, if it is connected and between any two vertices there are at most k geodesics. It is shown that any hyperbolic group with a k-geodetic Cayley graph is virtually-free. Furthermore, in such a group the centralizer of any infinite order element is an infinite cyclic group. These results were known previously only in the case that k=1. A key tool used to develop
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On the induced partial action of a quotient group and a structure theorem for a partial Galois extension Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-27 Jung-Miao Kuo, George Szeto
Let S be a ring with a partial action α of a finite group G. We determine when a quotient group of G gives rise to a partial action induced by α on a subring of S. As an application, we show that if S/Sα is an α-partial Galois extension and K is a normal subgroup of G, then under certain conditions SαK/Sα under the partial action of G/K induced by α, denoted by αG/K, is a partial Galois extension.
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ℵ0-Distributive modules and rings Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-20 Askar Tuganbaev
Let A be a ring with minimum condition on principal right ideals. It is proved that countably distributive right (left) A-modules coincide with Artinian (Noetherian) right (left) A-modules. Rings, over which all right modules are ℵ0-distributive coincide with rings of finite representation type. Rings, whose right modules are semidistributive, coincide with Kawada rings, over basis rings of which all
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On the number of tilting modules over a class of Auslander algebras Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-19 D. Chen, X. Zhang
Let Λ be a radical square zero algebra of a Dynkin quiver and let Γ be the Auslander algebra of Λ. Then the number of tilting right Γ-modules is 2m−1 if Λ is of Am type for m≥1. Otherwise, the number of tilting right Γ-modules is 2m−3×14 if Λ is either of Dm type for m≥4 or of Em type for m=6,7,8.
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A B-infinity algebra structure of singular Hochschild complex Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-14 Jun Qiu, Yu Wang
In this paper, we calculate the low order relations of B∞-algebra and introduce the bibrace algebra. It can be applied to the B∞-algebras of the (co)Hochschild cochain complex and the singular Hochschild complex of an algebra.
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Finite groups in which every maximal subgroup is nilpotent or normal or has p′-order Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-13 Jiangtao Shi, Na Li, Rulin Shen
Let G be a finite group and p a fixed prime divisor of |G|. We prove that if every maximal subgroup of G is nilpotent, or normal, or has p′-order, then (1) G is solvable; (2) G has a Sylow tower; (3) there exists at most one prime divisor q≠p of |G| such that G is neither q-nilpotent nor q-closed.
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Construction of symmetric cubic surfaces Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-12 Michela Brundu, Alessandro Logar, Federico Polli
We consider the action of the group PGL4(K) on the smooth cubic surfaces of ℙK3 (K an algebraically closed field of characteristic zero). We classify, in an explicit way, all the smooth cubic surfaces with nontrivial stabilizer, the corresponding stabilizers and obtain a geometric description of each group in terms of permutations of the Eckardt points, of the 27 lines or of the 45 tritangent planes
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Virtually unipotent curves in some non-NPC graph manifolds Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-10 Sami Douba
Let M be a graph manifold containing a single JSJ torus T and whose JSJ blocks are of the form Σ×S1, where Σ is a compact orientable surface with boundary. We show that if M does not admit a Riemannian metric of everywhere nonpositive sectional curvature, then there is an essential curve on T such that any finite-dimensional linear representation of π1(M) maps an element representing that curve to
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Semigroups locally embeddable into the class of finite semigroups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-08 D. Kudryavtsev
In this paper the concept of local embeddability into finite structures (being LEF) is examined for the class of semigroups. The established results include the connections to the previously studied class of LEF groups, residual finiteness, linear semigroups and the preservation of being LEF under certain semigroup constructions, such as adjoining zero or identity and taking direct, semidirect and
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On lax epimorphisms of partially ordered monoids Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-07-05 N. Sohail, A. H. Shah, S. A. Ahangar
Epimorphisms in the category of partially ordered monoids may not be surjective. We prove that lax epimorphisms in the category of partially ordered monoids are surjective. We further show that lax epimorphisms in the said category coincide with coinserters. Our results also generalize to partially ordered semigroups.
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A classification of the finite 2-generator cyclic-by-abelian groups of prime-power order Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-30 Osnel Broche, Diego García-Lucas, Ángel del Río
We classify the finite 2-generator cyclic-by-abelian groups of prime-power order. We associate to each such group G a list inv(G) of numerical group invariants which determines the isomorphism type of G. Then we describe the set formed by all the possible values of inv(G). This allows us to develop practical algorithms to construct all finite non-Abelian 2-generator cyclic-by-abelian groups of a given
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Free weighted (modified) differential algebras, free (modified) Rota–Baxter algebras and Gröbner–Shirshov bases Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-30 Zhicheng Zhu, Huhu Zhang, Xing Gao
In this paper, we obtain, respectively, some new linear bases of free nonunitary (modified) weighted differential algebras and free nonunitary (modified) Rota–Baxter algebras, in terms of the method of Gröbner–Shirshov bases.
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Super-biderivations on the planar Galilean conformal superalgebra Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-30 Ziyan Zuo, Jiancai Sun
Let 𝔤 be the planar Galilean conformal superalgebra. In this paper, we determine all the super-skewsymmetric super-biderivations of 𝔤. We find that every super-skewsymmetric super-biderivation of the planar Galilean conformal superalgebra is inner.
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Regular semigroups weakly generated by idempotents Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-30 Luís Oliveira
A regular semigroup is weakly generated by a set X if it has no proper regular subsemigroup containing X. In this paper, we study the regular semigroups weakly generated by idempotents. We show there exists a regular semigroup FI(X) weakly generated by |X| idempotents such that all other regular semigroups weakly generated by |X| idempotents are homomorphic images of FI(X). The semigroup FI(X) is defined
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The isomorphism problem of projective schemes and related algorithmic problems Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-30 Takehiko Yasuda
We discuss the isomorphism problem of projective schemes; given two projective schemes, can we algorithmically decide whether they are isomorphic? We give affirmative answers in the case of one-dimensional projective schemes, the case of smooth irreducible varieties with a big canonical sheaf or a big anti-canonical sheaf, and the case of K3 surfaces with a finite automorphism group. As related algorithmic
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Properties of symbolic powers of edge ideals of weighted oriented graphs Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-30 Mousumi Mandal, Dipak Kumar Pradhan
Let D be a weighted oriented graph and I(D) be its edge ideal. We provide one method to find all the minimal generators of I⊆C, where C is a maximal strong vertex cover of D and I⊆C is the intersections of irreducible ideals associated to the strong vertex covers contained in C. If D′ is an induced digraph of D, under a certain condition on the strong vertex covers of D′ and D, we show that I(D′)(s)≠I(D′)s
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Certain endomorphism rings of local cohomology modules and Lyubeznik numbers Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-29 Alberto F. Boix, Majid Eghbali
The goal of this paper is twofold: on the one hand, motivated by questions raised by Schenzel, we explore situations where the Hartshorne–Lichtenbaum Vanishing theorem for local cohomology fails, leading us to simpler expressions of certain local cohomology modules. As application, we give new expressions of the endomorphism ring of these modules. On the other hand, building upon previous work by Àlvarez
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Tate–Shafarevich groups and algebras Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-29 Boris Kunyavskiĭ, Vadim Z. Ostapenko
The Tate–Shafarevich set of a group G defined by Takashi Ono coincides, in the case where G is finite, with the group of outer class-preserving automorphisms of G introduced by Burnside. We consider analogs of this important group-theoretic object for Lie algebras and associative algebras and establish some new structure properties thereof. We also discuss open problems and eventual generalizations
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Classifying word problems of finitely generated algebras via computable reducibility Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-21 Valentino Delle Rose, Luca San Mauro, Andrea Sorbi
We contribute to a recent research program which aims at revisiting the study of the complexity of word problems, a major area of research in combinatorial algebra, through the lens of the theory of computably enumerable equivalence relations (ceers), which has considerably grown in recent times. To pursue our analysis, we rely on the most popular way of assessing the complexity of ceers, that is via
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Formal matrix rings: Automorphisms Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-12 Piotr Krylov, Askar Tuganbaev
Automorphism groups of formal matrix algebras with zero trace ideals are studied. Such an algebra is represented as a splitting extension of some ring by some nilpotent ideal. Using this extension, the study of the structure of the automorphism group of an algebra in a certain sense is reduced to the study of the structure of some its subgroups and quotient groups. Then the structure of these subgroups
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The lattice of clones of self-dual operations collapsed Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-08 Manuel Bodirsky, Albert Vucaj, Dmitriy Zhuk
We prove that there are continuum many clones on a three-element set even if they are considered up to homomorphic equivalence. The clones we use to prove this fact are clones consisting of self-dual operations, i.e. operations that preserve the relation {(0,1),(1,2),(2,0)}. However, there are only countably many such clones when considered up to equivalence with respect to minor-preserving maps instead
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Pure projective, pure injective and FP-injective modules over trivial ring extensions Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-06-08 Lixin Mao
Let R⋉M be a trivial extension of a ring R by an R-R-bimodule M. We first study the properties of pure projective and pure injective modules over R⋉M. Then we characterize FP-injective modules over R⋉M. Finally some applications are given to Morita context rings.
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Finitely generated dyadic convex sets Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-05-11 K. Matczak, A. Mućka, A. B. Romanowska
Dyadic rationals are rationals whose denominator is a power of 2. We define dyadic n-dimensional convex sets as the intersections with n-dimensional dyadic space of an n-dimensional real convex set. Such a dyadic convex set is said to be a dyadic n-dimensional polytope if the real convex set is a polytope whose vertices lie in the dyadic space. Dyadic convex sets are described as subreducts (subalgebras
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Finite groups satisfying the independence property Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-29 Saul D. Freedman, Andrea Lucchini, Daniele Nemmi, Colva M. Roney-Dougal
We say that a finite group G satisfies the independence property if, for every pair of distinct elements x and y of G, either {x,y} is contained in a minimal generating set for G or one of x and y is a power of the other. We give a complete classification of the finite groups with this property, and in particular prove that every such group is supersoluble. A key ingredient of our proof is a theorem
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The Yang–Baxter equation and Thompson’s group F Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-28 Fabienne Chouraqui
We define non-degenerate involutive partial solutions as a generalization of non-degenerate involutive set-theoretical solutions of the quantum Yang–Baxter equation (QYBE). The induced operator is not a classical solution of the QYBE, but a braiding operator as in conformal field theory. We define the structure inverse monoid of a non-degenerate involutive partial solution and prove that if the partial
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Knapsack and the power word problem in solvable Baumslag–Solitar groups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-21 Moses Ganardi, Markus Lohrey, Georg Zetzsche
We prove that the power word problem for certain metabelian subgroups of GL(2,ℂ) (including the solvable Baumslag–Solitar groups BS(1,q)=〈a,t|tat−1=aq〉) belongs to the circuit complexity class TC0. In the power word problem, the input consists of group elements g1,…,gd and binary encoded integers n1,…,nd and it is asked whether g1n1⋯gdnd=1 holds. Moreover, we prove that the knapsack problem for BS(1
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Chordal graphs, higher independence and vertex decomposable complexes Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-12 Fred M. Abdelmalek, Priyavrat Deshpande, Shuchita Goyal, Amit Roy, Anurag Singh
Given a finite simple undirected graph G there is a simplicial complex Ind(G), called the independence complex, whose faces correspond to the independent sets of G. This is a well-studied concept because it provides a fertile ground for interactions between commutative algebra, graph theory and algebraic topology. In this paper, we consider a generalization of independence complex. Given r≥1, a subset
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Saxl graphs of primitive affine groups with sporadic point stabilizers Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-11 Melissa Lee, Tomasz Popiel
Let G be a permutation group on a set Ω. A base for G is a subset of Ω whose pointwise stabilizer is trivial, and the base size of G is the minimal cardinality of a base for G. If G has base size 2, then the corresponding Saxl graph Σ(G) has vertex set Ω and two vertices are adjacent if and only if they form a base for G. A recent conjecture of Burness and Giudici states that if G is a finite primitive
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Strongly quasiconvex subgroups in amalgams and HNN extension Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-08 Hoang Thanh Nguyen, Hung Cong Tran
In this paper, we give a condition under which strong quasiconvexity in a finitely generated group is preserved under amalgams and HNN extension.
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On the transition monoid of the Stallings automaton of a subgroup of a free group Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-06 Inês F. Guimarães
Birget, Margolis, Meakin and Weil proved that a finitely generated subgroup K of a free group is pure if and only if the transition monoid M (K) of its Stallings automaton is aperiodic. In this paper, we establish further connections between algebraic properties of K and algebraic properties of M (K). We mainly focus on the cases where M (K) belongs to the pseudovariety of finite monoids all of whose
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Relative Maltsev definability of some commutator properties Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-04 Keith A. Kearnes
We show that, when restricted to the class of varieties that have a Taylor term, several commutator properties are definable by Maltsev conditions.
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On retracts determinating commutative trusses Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-04-04 R. R. Andruszkiewicz, K. Pryszczepko
This paper is devoted to study some relationships of trusses with rings. We characterize abelian groups A such that every truss with retract A has exactly two non-commutative multiplications. We describe commutative rings with nontrivial multiplication having non-commutative extension by the ring of integers.
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Automorphisms of affine Veronese surfaces Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-03-29 Bakhyt Aitzhanova, Ualbai Umirbaev
We prove that every derivation and every locally nilpotent derivation of the subalgebra K[xn,xn−1y,…,xyn−1,yn], where n≥2, of the polynomial algebra K[x,y] in two variables over a field K of characteristic zero is induced by a derivation and a locally nilpotent derivation of K[x,y], respectively. Moreover, we prove that every automorphism of K[xn,xn−1y,…,xyn−1,yn] over an algebraically closed field
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Non-colorable hierarchically hyperbolic groups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-03-18 Mark Hagen
We exhibit a hierarchically hyperbolic group for which no hierarchically hyperbolic structure is colorable, answering an (implicit) question of Durham–Minsky–Sisto.
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Regularity of powers of cover ideals of bipartite graphs Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-03-11 Nguyen Thu Hang, Truong Thi Hien
Let G=(V,E) be a bipartite graph over the vertex set V={1,…,r} and let J=J(G) be the cover ideal of G in the polynomial ring R=K[x1,…,xr]. It is known that there are integers b and t0 such that regJt=d(J)t+b is a linear function in t for all t≥t0. In this paper, we give effective bounds for b and t0.
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Degree 2 transformation semigroups as continuous maps on graphs: Complexity and examples Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-02-16 Stuart Margolis, John Rhodes
In this paper, we give a number of illuminating examples of transformation semigroups of degree 2 acting on graphs by functions that preserve vertices and edges by inverse image. It is known that the complexity of such a transformation semigroup is at most 2. We give examples that use sophisticated lower bounds to complexity to distinguish between complexity 1 and complexity 2.
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Lattice characterization of some classes of groups by series of subgroups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-01-25 Milan Grulović, Jelena Jovanović, Branimir Šešelja, Andreja Tepavčević
In this paper, we characterize several classes of groups by the properties of their weak congruence lattices. Namely, we give necessary and sufficient conditions for the weak congruence lattice of a group, under which this group is a T-group, T∗-group, metacyclic, cocyclic, hyperabelian, polycyclic, N-group and Ñ-group. We also discuss groups for which all subgroups are simple, like the Tarski monsters
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ℤ2-gradings and minimal varieties of ℤ2-graded PI algebras Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-01-19 Danilo Vilela Avelar, Viviane Ribeiro Tomaz da Silva
Let F be an algebraically closed field of characteristic zero and let A be a minimal superalgebra with semisimple part Ass=A1⊕⋯⊕An, where each Ai is a simple superalgebra. We say that A is r-special if n≥3 and there exists 1
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On the primality and elasticity of algebraic valuations of cyclic free semirings Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-01-14 Nancy Jiang, Bangzheng Li, Sophie Zhu
A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number α, the additive monoid Mα of the evaluation semiring ℕ0[α] is atomic. The atomic structure of both the additive and the multiplicative monoids of ℕ0[α] has been the subject of several recent papers. Here we focus on the monoids Mα, and we
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Cogrowth series for free products of finite groups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2023-01-14 Jason Bell, Haggai Liu, Marni Mishna
Given a finitely generated group with generating set S, we study the cogrowth sequence, which is the number of words of length n over the alphabet S that are equal to the identity in the group. This is related to the probability of return for walks on the corresponding Cayley graph. Muller and Schupp proved the generating function of the sequence is algebraic when G has a finite-index-free subgroup
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Numerical semigroups without consecutive small elements Int. J. Algebra Comput. (IF 0.8) Pub Date : 2022-12-09 José C. Rosales, Manuel B. Branco, Márcio A. Traesel
In this work, we study A-semigroups, that is, numerical semigroups which have no consecutive elements less than the Frobenius number. We give algorithms that allow computation of the whole set of A-semigroups with a given genus, multiplicity and Frobenius number and from this we study interesting families of A-semigroups which are Frobenius varieties, pseudo-varieties; R-varieties.
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Cross-connection structure of locally inverse semigroups Int. J. Algebra Comput. (IF 0.8) Pub Date : 2022-12-09 P. A. Azeef Muhammed, Mikhail V. Volkov, Karl Auinger
Locally inverse semigroups are regular semigroups whose idempotents form pseudo-semilattices. We characterize the categories that correspond to locally inverse semigroups in the realm of Nambooripad’s cross-connection theory. Further, we specialize our cross-connection description of locally inverse semigroups to inverse semigroups and completely 0-simple semigroups, obtaining structure theorems for
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Algorithmic local monomialization of a binomial: A comparison of different approaches Int. J. Algebra Comput. (IF 0.8) Pub Date : 2022-12-09 Sabrina Alexandra Gaube, Bernd Schober
We investigate different approaches to transform a given binomial into a monomial via blowing up appropriate centers. In particular, we develop explicit implementations in Singular, which allow to make a comparison on the basis of numerous examples. We focus on a local variant, where centers are not required to be chosen globally. Moreover, we do not necessarily demand that centers are contained in
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Rational function semifields of tropical curves are finitely generated over the tropical semifield Int. J. Algebra Comput. (IF 0.8) Pub Date : 2022-11-30 Song JuAe
We prove that the rational function semifield of a tropical curve is finitely generated as a semifield over the tropical semifield T:=(R∪{−∞},max,+) by giving a specific finite generating set. Also, we show that for a finite harmonic morphism between tropical curves φ:Γ→Γ′, the rational function semifield of Γ is finitely generated as a φ∗(Rat(Γ′))-algebra, where φ∗(Rat(Γ′)) stands for the pull-back
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The ℛ-height of semigroups and their bi-ideals Int. J. Algebra Comput. (IF 0.8) Pub Date : 2022-11-28 Craig Miller
The ℛ-height of a semigroup S is the height of the poset of ℛ-classes of S. Given a semigroup S with finite ℛ-height, we establish bounds on the ℛ-height of bi-ideals, one-sided ideals and two-sided ideals; in particular, these substructures inherit the property of having finite ℛ-height. We then investigate whether these bounds can be attained.