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  • Metabelian groups: Full-rank presentations, randomness and Diophantine problems
    J. Group Theory (IF 0.466) Pub Date : 2020-12-09
    Albert Garreta; Leire Legarreta; Alexei Miasnikov; Denis Ovchinnikov

    We study metabelian groups 𝐺 given by full rank finite presentations ⟨A∣R⟩M in the variety ℳ of metabelian groups. We prove that 𝐺 is a product of a free metabelian subgroup of rank max⁡{0,|A|-|R|} and a virtually abelian normal subgroup, and that if |R|≤|A|-2, then the Diophantine problem of 𝐺 is undecidable, while it is decidable if |R|≥|A|. We further prove that if |R|≤|A|-1, then, in any direct

    更新日期:2021-01-19
  • Nilpotence relations in products of groups
    J. Group Theory (IF 0.466) Pub Date : 2020-12-16
    Giulio Francalanci

    Two subgroups 𝐴 and 𝐵 of a group 𝐺 are said to be 𝒩-connected if, for all 𝑎 in 𝐴 and 𝑏 in 𝐵, the subgroup generated by 𝑎 and 𝑏 is a nilpotent group. In this paper, we study the structure of a group 𝐺 assuming that G=A⁢B and 𝐴 and 𝐵 are 𝒩-connected subgroups satisfying Max or Min.

    更新日期:2021-01-19
  • On the minimal degree of a transitive permutation group with stabilizer a 2-group
    J. Group Theory (IF 0.466) Pub Date : 2020-12-18
    Primož Potočnik; Pablo Spiga

    The minimal degree of a permutation group 𝐺 is defined as the minimal number of non-fixed points of a non-trivial element of 𝐺. In this paper, we show that if 𝐺 is a transitive permutation group of degree 𝑛 having no non-trivial normal 2-subgroups such that the stabilizer of a point is a 2-group, then the minimal degree of 𝐺 is at least 23⁢n. The proof depends on the classification of finite simple

    更新日期:2021-01-19
  • On the stabilisers of points in groups with micro-supported actions
    J. Group Theory (IF 0.466) Pub Date : 2020-12-22
    Dominik Francoeur

    Given a group 𝐺 of homeomorphisms of a first-countable Hausdorff space 𝒳, we prove that if the action of 𝐺 on 𝒳 is minimal and has rigid stabilisers that act locally minimally, then the neighbourhood stabilisers of any two points in 𝒳 are conjugated by a homeomorphism of 𝒳. This allows us to study stabilisers of points in many classes of groups, such as topological full groups of Cantor minimal

    更新日期:2021-01-19
  • The groups (2, 𝑚 𝑛, 𝑘 1, 𝑞): Finiteness and homotopy
    J. Group Theory (IF 0.466) Pub Date : 2020-12-22
    Edward Bennett; Mark Dennis; Martin Edjvet

    We initiate the study of the groups (l,m∣n,k∣p,q) defined by the presentation ⟨a,b∣al,bm,(a⁢b)n,(ap⁢bq)k⟩. When p=1 and q=m-1, we obtain the group (l,m∣n,k), first systematically studied by Coxeter in 1939. In this paper, we restrict ourselves to the case l=2 and 1n+1k≤12 and give a complete determination as to which of the resulting groups are finite. We also, under certain broadly defined conditions

    更新日期:2021-01-19
  • Subnormality and residuals for saturated formations: A generalization of Schenkman’s theorem
    J. Group Theory (IF 0.466) Pub Date : 2020-12-23
    Stefanos Aivazidis; Inna N. Safonova; Alexander N. Skiba

    Let 𝐺 be a finite group, and let 𝔉 be a hereditary saturated formation. We denote by ZF⁢(G) the product of all normal subgroups 𝑁 of 𝐺 such that every chief factor H/K of 𝐺 below 𝑁 is 𝔉-central in 𝐺, that is, (H/K)⋊(G/CG⁢(H/K))∈F. A subgroup A⩽G is said to be 𝔉-subnormal in the sense of Kegel, or 𝐾-𝔉-subnormal in 𝐺, if there is a subgroup chain A=A0⩽A1⩽⋯⩽An=G such that either Ai-1⁢⊴⁢Ai

    更新日期:2021-01-19
  • Odd order products of conjugate involutions in~linear groups over GF(2𝑎)
    J. Group Theory (IF 0.466) Pub Date : 2021-01-14
    John J. Ballantyne; Peter J. Rowley

    Let 𝐺 be isomorphic to GLn⁢(q), SLn⁢(q), PGLn⁢(q) or PSLn⁢(q), where q=2a. If 𝑡 is an involution lying in a 𝐺-conjugacy class 𝑋, then, for arbitrary 𝑛, we show that, as 𝑞 becomes large, the proportion of elements of 𝑋 which have odd order product with 𝑡 tends to 1. Furthermore, for 𝑛 at most 4, we give formulae for the number of elements in 𝑋 which have odd order product with 𝑡, in terms

    更新日期:2021-01-19
  • Exponent of a finite group admitting a coprime automorphism of prime order
    J. Group Theory (IF 0.466) Pub Date : 2020-12-09
    Sara Rodrigues; Pavel Shumyatsky

    Let 𝐺 be a finite group admitting an automorphism 𝜙 of prime order 𝑝 such that (|G|,p)=1. It is shown that if the fixed-point subgroup for 𝜙 has rank 𝑟 and (x-1⁢xϕ)e=1 for each x∈G, then the exponent of [G,ϕ] is (e,p,r)-bounded.

    更新日期:2021-01-14
  • New Lie products for groups and their automorphisms
    J. Group Theory (IF 0.466) Pub Date : 2021-01-12
    James B. Wilson

    We generalize the common notion of descending and ascending central series. The descending approach determines a naturally graded Lie ring and the ascending version determines a graded module for this ring. We also link derivations of these rings to the automorphisms of a group. This process uncovers new structure in 4/5 of the approximately 11.8 million groups of size at most 1000 and beyond that

    更新日期:2021-01-14
  • On the holomorph of finite semisimple groups
    J. Group Theory (IF 0.466) Pub Date : 2020-12-02
    Russell D. Blyth; Francesco Fumagalli

    Given a finite nonabelian semisimple group 𝐺, we describe those groups that have the same holomorph as 𝐺, that is, those regular subgroups N≃G of S⁢(G), the group of permutations on the set 𝐺, such that NS⁢(G)⁢(N)=NS⁢(G)⁢(ρ⁢(G)), where 𝜌 is the right regular representation of 𝐺.

    更新日期:2021-01-13
  • Frontmatter
    J. Group Theory (IF 0.466) Pub Date : 2021-01-01

    Journal Name: Journal of Group Theory Volume: 24 Issue: 1 Pages: i-iv

    更新日期:2020-12-31
  • Groups that have a partition by commuting subsets
    J. Group Theory (IF 0.466) Pub Date : 2020-11-04
    Tuval Foguel; Josh Hiller; Mark L. Lewis; Alireza Moghaddamfar

    Let 𝐺 be a nonabelian group. We say that 𝐺 has an abelian partition if there exists a partition of 𝐺 into commuting subsets A1,A2,…,An of 𝐺 such that |Ai|⩾2 for each i=1,2,…,n. This paper investigates problems relating to groups with abelian partitions. Among other results, we show that every finite group is isomorphic to a subgroup of a group with an abelian partition and also isomorphic to a

    更新日期:2020-12-30
  • Quotient-transitivity and cyclic subgroup-transitivity
    J. Group Theory (IF 0.466) Pub Date : 2020-11-05
    Brendan Goldsmith; Ketao Gong

    We introduce two new notions of transitivity for Abelian 𝑝-groups based on isomorphism of quotients rather than the classical use of equality of height sequences associated with Abelian 𝑝-group theory. Unlike the classical theory where “most” groups are transitive, these new notions lead to much smaller classes, but even these classes are sufficiently large to be interesting.

    更新日期:2020-12-30
  • 𝒫-characters and the structure of finite solvable groups
    J. Group Theory (IF 0.466) Pub Date : 2020-11-06
    Jiakuan Lu; Kaisun Wu; Wei Meng

    Let 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1H)G for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.

    更新日期:2020-12-30
  • The subnormal structure of classical-like groups over commutative rings
    J. Group Theory (IF 0.466) Pub Date : 2020-11-14
    Raimund Preusser

    Let 𝑛 be an integer greater than or equal to 3, and let (R,Δ) be a Hermitian form ring, where 𝑅 is commutative. We prove that if 𝐻 is a subgroup of the odd-dimensional unitary group U2⁢n+1⁡(R,Δ) normalised by a relative elementary subgroup EU2⁢n+1⁡((R,Δ),(I,Ω)), then there is an odd form ideal (J,Σ) such that

    更新日期:2020-12-30
  • A classification of the abelian minimal closed normal subgroups of locally compact second-countable groups
    J. Group Theory (IF 0.466) Pub Date : 2020-11-17
    Colin D. Reid

    We classify the locally compact second-countable (l.c.s.c.) groups 𝐴 that are abelian and topologically characteristically simple. All such groups 𝐴 occur as the monolith of some soluble l.c.s.c. group 𝐺 of derived length at most 3; with known exceptions (specifically, when 𝐴 is Qn or its dual for some n∈N), we can take 𝐺 to be compactly generated. This amounts to a classification of the possible

    更新日期:2020-12-30
  • Commuting graph of 𝐴-orbits
    J. Group Theory (IF 0.466) Pub Date : 2020-11-21
    İsmail Ş. Güloğlu; Gülin Ercan

    Let 𝐴 be a finite group acting by automorphisms on the finite group 𝐺. We introduce the commuting graph Γ⁢(G,A) of this action and study some questions related to the structure of 𝐺 under certain graph theoretical conditions on Γ⁢(G,A).

    更新日期:2020-12-30
  • TI subgroups and depth 3 subgroups in simple Suzuki groups
    J. Group Theory (IF 0.466) Pub Date : 2020-12-15
    Hayder Abbas Janabi; László Héthelyi; Erzsébet Horváth

    In this paper, we determine the TI subgroups of the simple Suzuki groups Sz⁢(q). More generally, we determine those nontrivial subgroups that are disjoint from some of their conjugates. It turns out that the latter are exactly those subgroups that have ordinary depth 3. The Sylow 2-subgroups of simple Suzuki groups belong to the class of so-called Suzuki 2-groups, which have been studied extensively

    更新日期:2020-12-15
  • On a theorem of Ito and Szép
    J. Group Theory (IF 0.466) Pub Date : 2020-10-24
    Zhenfeng Wu; Wenbin Guo

    A subgroup 𝐻 of a group 𝐺 is said to be conditionally permutable (or 𝑐-permutable for short) in 𝐺 if, for every subgroup 𝑇 of 𝐺, there exists an element x∈G such that H⁢Tx=Tx⁢H. A subgroup 𝐻 of a group 𝐺 is said to be completely 𝑐-permutable in 𝐺 if, for every subgroup 𝑇 of 𝐺, the subgroups 𝐻 and 𝑇 are 𝑐-permutable in ⟨H,T⟩. In this paper, we prove that H/HG is nilpotent if 𝐻 is a completely

    更新日期:2020-11-15
  • A sharp upper bound for the size of Lusztig series
    J. Group Theory (IF 0.466) Pub Date : 2020-10-09
    Christine Bessenrodt; Alexandre Zalesski

    The paper is concerned with the character theory of finite groups of Lie type. The irreducible characters of a group 𝐺 of Lie type are partitioned in Lusztig series. We provide a simple formula for an upper bound of the maximal size of a Lusztig series for classical groups with connected center; this is expressed for each group 𝐺 in terms of its Lie rank and defining characteristic. When 𝐺 is specified

    更新日期:2020-11-06
  • The profinite completion of multi-EGS groups
    J. Group Theory (IF 0.466) Pub Date : 2020-11-05
    Anitha Thillaisundaram; Jone Uria-Albizuri

    The class of multi-EGS groups is a generalisation of the well-known Grigorchuk–Gupta–Sidki (GGS-)groups. Here we classify branch multi-EGS groups with the congruence subgroup property and determine the profinite completion of all branch multi-EGS groups. Additionally, our results show that branch multi-EGS groups are just infinite.

    更新日期:2020-11-06
  • Fibonacci groups 𝐹(2, 𝑛) are hyperbolic for 𝑛 odd and 𝑛 ≥ 11
    J. Group Theory (IF 0.466) Pub Date : 2020-10-03
    Christopher P. Chalk

    We prove that the Fibonacci group F⁢(2,n) for 𝑛 odd and n≥11 is hyperbolic. We do this by applying a curvature argument to an arbitrary van Kampen diagram of F⁢(2,n) and show that it satisfies a linear isoperimetric inequality. It then follows that F⁢(2,n) is hyperbolic.

    更新日期:2020-11-04
  • Serre’s Property (FA) for automorphism groups of free products
    J. Group Theory (IF 0.466) Pub Date : 2020-10-29
    Naomi Andrew

    We provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products

    更新日期:2020-10-30
  • Frontmatter
    J. Group Theory (IF 0.466) Pub Date : 2020-11-01

    Journal Name: Journal of Group Theory Volume: 23 Issue: 6 Pages: i-iv

    更新日期:2020-10-30
  • Supercharacter theories for algebra group extensions
    J. Group Theory (IF 0.466) Pub Date : 2020-10-01
    Aleksandr Nikolaevich Panov

    We construct a few supercharacter theories for finite semidirect products where the normal subgroup is of algebra group type. In the case of algebra groups, these supercharacter theories coincide with those of P. Diaconis and I. M. Isaacs. For the parabolic subgroups of GL⁢(n,Fq), the supercharacters and superclasses are classified.

    更新日期:2020-10-02
  • Obstruction to a Higman embedding theorem for residually finite groups with solvable word problem
    J. Group Theory (IF 0.466) Pub Date : 2020-10-01
    Emmanuel Rauzy

    We prove that, for a finitely generated residually finite group, having solvable word problem is not a sufficient condition to be a subgroup of a finitely presented residually finite group. The obstruction is given by a residually finite group with solvable word problem for which there is no effective method that allows, given some non-identity element, to find a morphism onto a finite group in which

    更新日期:2020-10-02
  • Finite 𝑝-groups all of whose 𝓐2-subgroups are generated by two elements
    J. Group Theory (IF 0.466) Pub Date : 2020-09-09
    Lihua Zhang; Junqiang Zhang

    Assume G is a finite p-group. We prove that if all 𝒜2-subgroups of G are generated by two elements, then so are all non-abelian subgroups of G. By using this result, we classify the p-groups which have at least two 𝒜1-subgroups and in which the intersection of every pair of distinct 𝒜1-subgroups equals the intersection of all the 𝒜1-subgroups. It turns out that such p-groups are the finite p-groups

    更新日期:2020-09-09
  • Even character degrees and normal Sylow 2-subgroups
    J. Group Theory (IF 0.466) Pub Date : 2020-09-09
    Hongfei Pan; Nguyen Ngoc Hung; Shuqin Dong

    The Ito–Michler theorem on character degrees states that if a prime p does not divide the degree of any irreducible character of a finite group G, then G has a normal Sylow p-subgroup. We give some strengthened versions of this result for p=2 by considering linear characters and those of even degree.

    更新日期:2020-09-09
  • Frontmatter
    J. Group Theory (IF 0.466) Pub Date : 2020-09-01

    Journal Name: Journal of Group Theory Volume: 23 Issue: 5 Pages: i-iv

    更新日期:2020-09-01
  • Irreducible representations of Braid group 𝐵𝑛 of dimension 𝑛 + 1
    J. Group Theory (IF 0.466) Pub Date : 2020-08-25
    Inna Sysoeva

    We prove that there are no irreducible representations of Bn of dimension n+1 for n⩾10.

    更新日期:2020-08-25
  • Right-angled Artin groups and enhanced Koszul properties
    J. Group Theory (IF 0.466) Pub Date : 2020-08-25
    Alberto Cassella; Claudio Quadrelli

    Let 𝔽 be a finite field. We prove that the cohomology algebra H∙⁢(GΓ,𝔽) with coefficients in 𝔽 of a right-angled Artin group GΓ is a strongly Koszul algebra for every finite graph Γ. Moreover, H∙⁢(GΓ,𝔽) is a universally Koszul algebra if, and only if, the graph Γ associated to the group GΓ has the diagonal property. From this, we obtain several new examples of pro-p groups, for a prime number p

    更新日期:2020-08-25
  • Groups satisfying the double chain condition on non-subnormal subgroups
    J. Group Theory (IF 0.466) Pub Date : 2020-08-25
    Mattia Brescia

    If θ is a subgroup property, a group G is said to satisfy the double chain condition on θ-subgroups if it admits no infinite double sequences

    更新日期:2020-08-25
  • Generation of finite groups with cyclic Sylow subgroups
    J. Group Theory (IF 0.466) Pub Date : 2020-08-25
    Heiko Dietrich; Darren Low

    M. C. Slattery [Generation of groups of square-free order, J. Symbolic Comput.42 (2007), 6, 668–677] described computational methods to enumerate, construct and identify finite groups of squarefree order. We generalise Slattery’s result to the class of finite groups that have cyclic Sylow subgroups and provide an implementation for the computer algebra system GAP.

    更新日期:2020-08-25
  • A periodicity theorem for acylindrically hyperbolic groups
    J. Group Theory (IF 0.466) Pub Date : 2020-08-25
    Oleg Bogopolski

    We generalize a well-known periodicity lemma from the case of free groups to the case of acylindrically hyperbolic groups. This generalization has been used to describe solutions of certain equations in acylindrically hyperbolic groups and to characterize verbally closed finitely generated acylindrically hyperbolic subgroups of finitely presented groups.

    更新日期:2020-08-25
  • Local finiteness of the twisted Bruhat orders on affine Weyl groups
    J. Group Theory (IF 0.466) Pub Date : 2020-08-19
    Weijia Wang

    In this paper, we investigate various properties of strong and weak twisted Bruhat orders on a Coxeter group. In particular, we prove that any twisted strong Bruhat order on an affine Weyl group is locally finite, strengthening a result of Dyer [Quotients of twisted Bruhat orders, J. Algebra 163 1994, 3, 861–879]. We also show that, for a non-finite and non-cofinite biclosed set B in the positive system

    更新日期:2020-08-19
  • Invariable generation and wreath products
    J. Group Theory (IF 0.466) Pub Date : 2020-08-15
    Charles Garnet Cox

    Invariable generation is a topic that has predominantly been studied for finite groups. In 2014, Kantor, Lubotzky and Shalev produced extensive tools for investigating invariable generation for infinite groups. Since their paper, various authors have investigated the property for particular infinite groups or families of infinite groups. A group is invariably generated by a subset 𝑆 if replacing each

    更新日期:2020-08-15
  • The main decomposition of finite-dimensional protori
    J. Group Theory (IF 0.466) Pub Date : 2020-08-12
    Wayne Lewis; Peter Loth; Adolf Mader

    A protorus is a compact connected abelian group of finite dimension. We use a result on finite-rank torsion-free abelian groups and Pontryagin duality to considerably generalize a well-known factorization of a finite-dimensional protorus into a product of a torus and a torus free complementary factor. We also classify direct products of protori of dimension 1 by means of canonical “type” subgroups

    更新日期:2020-08-12
  • Growth rate for endomorphisms of finitely generated nilpotent groups
    J. Group Theory (IF 0.466) Pub Date : 2020-08-08
    Alexander Fel’shtyn; Jang Hyun Jo; Jong Bum Lee

    We prove that the growth rate of an endomorphism of a finitely generated nilpotent group is equal to the growth rate of the induced endomorphism on its abelianization, generalizing the corresponding result for an automorphism in [T. Koberda, Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups, In the Tradition of Ahlfors–Bers. VI, Contemp. Math. 590, American

    更新日期:2020-08-08
  • Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal
    J. Group Theory (IF 0.466) Pub Date : 2020-08-06
    Anatoly S. Kondrat’ev; Natalia V. Maslova; Danila O. Revin

    A subgroup H of a group G is said to be pronormal in G if H and Hg are conjugate in 〈H,Hg〉 for every g∈G. In this paper, we determine the finite simple groups of type E6⁢(q) and E62⁢(q) in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.

    更新日期:2020-08-06
  • On quasiprimitive edge-transitive graphs of odd order and twice prime valency
    J. Group Theory (IF 0.466) Pub Date : 2020-07-16
    Hong Ci Liao; Jing Jian Li; Zai Ping Lu

    A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let Γ be a connected graph of odd order and twice prime valency, and let G be a subgroup of the automorphism group of Γ. In the case where G acts transitively on the edge set and quasiprimitively

    更新日期:2020-07-16
  • Units and augmentation powers in integral group rings
    J. Group Theory (IF 0.466) Pub Date : 2020-07-16
    Sugandha Maheshwary; Inder Bir S. Passi

    The augmentation powers in an integral group ring ℤ⁢G induce a natural filtration of the unit group of ℤ⁢G analogous to the filtration of the group G given by its dimension series {Dn⁢(G)}n≥1. The purpose of the present article is to investigate this filtration, in particular, the triviality of its intersection.

    更新日期:2020-07-16
  • Character degrees in 𝜋-separable groups
    J. Group Theory (IF 0.466) Pub Date : 2020-07-10
    Nicola Grittini

    If a group G is π-separable, where π is a set of primes, the set of irreducible characters Bπ⁡(G)∪Bπ′⁡(G) can be defined. In this paper, we prove variants of some classical theorems in character theory, namely the theorem of Ito–Michler and Thompson’s theorem on character degrees, involving irreducible characters in the set Bπ⁡(G)∪Bπ′⁡(G).

    更新日期:2020-07-10
  • On the odd order composition factors of finite linear groups
    J. Group Theory (IF 0.466) Pub Date : 2020-07-10
    Alexander Betz; Max Chao-Haft; Ting Gong; Anthony Ter-Saakov; Yong Yang

    In this paper, we study the product of orders of composition factors of odd order in a composition series of a finite linear group. First we generalize a result by Manz and Wolf about the order of solvable linear groups of odd order. Then we use this result to find bounds for the product of orders of composition factors of odd order in a composition series of a finite linear group.

    更新日期:2020-07-10
  • The invariably generating graph of the alternating and symmetric groups
    J. Group Theory (IF 0.466) Pub Date : 2020-07-10
    Daniele Garzoni

    Given a finite group G, the invariably generating graph of G is defined as the undirected graph in which the vertices are the nontrivial conjugacy classes of G, and two classes are adjacent if and only if they invariably generate G. In this paper, we study this object for alternating and symmetric groups. The main result of the paper states that if we remove the isolated vertices from the graph, the

    更新日期:2020-07-10
  • Frontmatter
    J. Group Theory (IF 0.466) Pub Date : 2020-07-01

    Journal Name: Journal of Group Theory Volume: 23 Issue: 4 Pages: i-iv

    更新日期:2020-06-26
  • 𝑝-groups with exactly four codegrees
    J. Group Theory (IF 0.466) Pub Date : 2020-06-11
    Sarah Croome; Mark L. Lewis

    Let G be a p-group, and let χ be an irreducible character of G. The codegree of χ is given by |G:ker(χ)|/χ(1). Du and Lewis have shown that a p-group with exactly three codegrees has nilpotence class at most 2. Here we investigate p-groups with exactly four codegrees. If, in addition to having exactly four codegrees, G has two irreducible character degrees, G has largest irreducible character degree

    更新日期:2020-06-11
  • Conjugacy class sizes in arithmetic progression
    J. Group Theory (IF 0.466) Pub Date : 2020-06-11
    Mariagrazia Bianchi; Stephen P. Glasby; Cheryl E. Praeger

    Let cs⁢(G) denote the set of conjugacy class sizes of a group G, and let cs*⁢(G)=cs⁢(G)∖{1} be the sizes of non-central classes. We prove three results. We classify all finite groups for which (1) cs⁢(G)={a,a+d,…,a+r⁢d} is an arithmetic progression with r⩾2; (2) cs*⁢(G)={2,4,6} is the smallest case where cs*⁢(G) is an arithmetic progression of length more than 2 (our most substantial result); (3) the

    更新日期:2020-06-11
  • When a locally compact monothetic semigroup is compact
    J. Group Theory (IF 0.466) Pub Date : 2020-06-11
    Yevhen Zelenyuk; Yuliya Zelenyuk

    A semigroup endowed with a topology is monothetic if it contains a dense monogenic subsemigroup. A semigroup (group) endowed with a topology is semitopological (quasitopological) if the translations (the translations and the inversion) are continuous. If S is a nondiscrete monothetic semitopological semigroup, then the set S′ of all limit points of S is a closed ideal of S. Let S be a locally compact

    更新日期:2020-06-11
  • On the topology of geometric and rational orbits for algebraic group actions over valued fields
    J. Group Theory (IF 0.466) Pub Date : 2020-06-11
    Phuong Bac Dao

    In this note, we study the relationship between Zariski and relative closedness for actions of (smooth) algebraic groups defined over valued (mainly local) fields of any characteristic. In particular, we use some recent basic results regarding the completely reducible subgroups and cocharacter-closedness due to Bate–Herpel–Röhrle–Tange and Uchiyama to construct some actions of simple algebraic groups

    更新日期:2020-06-11
  • Group actions and non-vanishing elements in solvable groups
    J. Group Theory (IF 0.466) Pub Date : 2020-06-11
    Thomas R. Wolf

    For a solvable group, a theorem of Gaschutz shows that F⁢(G)/Φ⁢(G) is a direct sum of irreducible G-modules and a faithful G/F⁢(G)-module. If each of these irreducible modules is primitive, we show that every non-vanishing element of G lies in F⁢(G).

    更新日期:2020-06-11
  • Compact groups with many elements of bounded order
    J. Group Theory (IF 0.466) Pub Date : 2020-06-11
    Meisam Soleimani Malekan; Alireza Abdollahi; Mahdi Ebrahimi

    Lévai and Pyber proposed the following as a conjecture: Let G be a profinite group such that the set of solutions of the equation xn=1 has positive Haar measure. Then G has an open subgroup H and an element t such that all elements of the coset tH have order dividing n (see [V. D. Mazurov and E. I. Khukhro, Unsolved Problems in Group Theory. The Kourovka Notebook. No. 19, Russian Academy of Sciences

    更新日期:2020-06-11
  • Residual dimension of nilpotent groups
    J. Group Theory (IF 0.466) Pub Date : 2020-05-27
    Mark Pengitore

    The function FG⁢(n) gives the maximum order of a finite group needed to distinguish a nontrivial element of G from the identity with a surjective group morphism as one varies over nontrivial elements of word length at most n. In previous work [M. Pengitore, Effective separability of finitely generated nilpotent groups, New York J. Math. 24 2018, 83–145], the author claimed a characterization for FN⁢(n)

    更新日期:2020-05-27
  • Applying combinatorial results to products of conjugacy classes
    J. Group Theory (IF 0.466) Pub Date : 2020-05-20
    Rachel Deborah Camina

    Let K=xG be the conjugacy class of an element x of a group G, and suppose K is finite. We study the increasing sequence of natural numbers {|Kn|}n≥1 and consider restrictions on this sequence and the algebraic consequences. In particular, we prove that if |K2|<32⁢|K| or if |K4|<2⁢|K|, then Kn is a coset of the normal subgroup [x,G] for all n≥2 or 4, respectively. We then use these results to contribute

    更新日期:2020-05-20
  • Additivity of the algebraic entropy for locally finite groups with permutable finite subgroups
    J. Group Theory (IF 0.466) Pub Date : 2020-05-12
    Anna Giordano Bruno; Flavio Salizzoni

    Additivity with respect to exact sequences is, notoriously, a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by using the structure theorems for such groups in an essential way. On the other hand, a solvable counterexample was recently found, showing that it does not hold in general. Nevertheless, we give a rather short proof of the additivity

    更新日期:2020-05-12
  • On the triple tensor product of prime-power groups
    J. Group Theory (IF 0.466) Pub Date : 2020-05-12
    S. Hadi Jafari; Halimeh Hadizadeh

    Let G be a finite p-group, and let ⊗3G be its triple tensor product. In this paper, we obtain an upper bound for the order of ⊗3G, which sharpens the bound given by G. Ellis and A. McDermott, [Tensor products of prime-power groups, J. Pure Appl. Algebra 132 1998, 2, 119–128]. In particular, when G has a derived subgroup of order at most p, we classify those groups G for which the bound is attained

    更新日期:2020-05-12
  • On the supersolubility of a group with semisubnormal factors
    J. Group Theory (IF 0.466) Pub Date : 2020-05-12
    Victor S. Monakhov; Alexander A. Trofimuk

    A subgroup A of a group G is called seminormal in G if there exists a subgroup B such that G=A⁢B and AX is a subgroup of G for every subgroup X of B. We introduce the new concept that unites subnormality and seminormality. A subgroup A of a group G is called semisubnormal in G if A is subnormal in G or seminormal in G. A group G=A⁢B with semisubnormal supersoluble subgroups A and B is studied. The

    更新日期:2020-05-12
  • Classification of the affine structures of a generalized quaternion group of order ⩾32{\geqslant 32}
    J. Group Theory (IF 0.466) Pub Date : 2020-05-12
    Wolfgang Rump

    Based on computing evidence, Guarnieri and Vendramin conjectured that, for a generalized quaternion group G of order 2n⩾32, there are exactly seven isomorphism classes of braces with adjoint group G. The conjecture is proved in the paper.

    更新日期:2020-05-12
  • Some generalized characters associated to a transitive permutation group
    J. Group Theory (IF 0.466) Pub Date : 2020-05-01
    Wolfgang Knapp; Peter Schmid

    Let G be a finite transitive permutation group of degree n, with point stabilizer H≠1 and permutation character π. For every positive integer t, we consider the generalized character ψt=ρG-t⁢(π-1G), where ρG is the regular character of G and 1G the 1-character. We give necessary and sufficient conditions on t (and G) which guarantee that ψt is a character of G. A necessary condition is that t≤min⁡{n-1

    更新日期:2020-05-01
  • A note on vertices of indecomposable tensor products
    J. Group Theory (IF 0.466) Pub Date : 2020-05-01
    Markus Linckelmann

    G. Navarro raised the question of when two vertices of two indecomposable modules over a finite group algebra generate a Sylow p-subgroup. The present note provides a sufficient criterion for this to happen. This generalises a result by Navarro for simple modules over finite p-solvable groups, which is the main motivation for this note.

    更新日期:2020-05-01
  • Frontmatter
    J. Group Theory (IF 0.466) Pub Date : 2020-05-01

    Journal Name: Journal of Group Theory Volume: 23 Issue: 3 Pages: i-iv

    更新日期:2020-05-01
Contents have been reproduced by permission of the publishers.
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