A profinite group is index-stable if any two isomorphic open subgroups have the same index. Let p be a prime, and let G be a compact p-adic analytic group with associated \(\mathbb {Q}_p\)-Lie algebra \(\mathcal {L}(G)\). We prove that G is index-stable whenever \(\mathcal {L}(G)\) is semisimple. In particular, a just-infinite compact p-adic analytic group is index-stable if and only if it is not virtually

Let G be a finite group of even order that has no 2-rank 1. We will prove, using only elementary methods, that there is an involution \(t \in G\) such that \(|G| < |C_{G}(t)|^{6}\).

Let A be a PI-algebra. If A is an associative algebra, the sequence of codimensions \(c_n(A), n=1,2,\ldots ,\) of A is asymptotically non-decreasing. For the non-associative case, there are examples of PI-algebras whose sequence of codimensions is not eventually non-decreasing. For a associative PI-algebra A with involution \(*: A\rightarrow A\), it was recently shown that its sequence of \(*\)-codimensions

We study a geometric flow on curves, immersed in \({\mathbb {R}}^3\), that have strictly positive torsion. The evolution equation is given by $$\begin{aligned} X_{t}=\frac{1}{\sqrt{\tau }} \mathbf{B} \end{aligned}$$ where \(\tau \) is the torsion and \(\mathbf{B} \) is the unit binormal vector. In the case of constant curvature, we find all of the stationary solutions and linearize the PDE for the

We study \((\sigma ,\tau )\)-derivations of a group ring RG where G is a group with center having finite index in G and R is a semiprime ring with 1 such that either R has no torsion elements or that if R has p-torsion elements, then p does not divide the order of G and let \(\sigma ,\tau \) be R-linear endomorphisms of RG fixing the center of RG pointwise. We generalize Main Theorem 1.1 of Chaudhuri

We investigate the behavior of the second fundamental form of an isometric immersion of a space form with negative curvature into a space form so that the extrinsic curvature is negative. If the immersion has flat normal bundle, we prove that its second fundamental form grows exponentially.

A closed Riemann surface S (of genus at least one) is called an origami curve if it admits a non-constant holomorphic map \(\beta :S \rightarrow E\) with at most one branch value, where E is a genus one Riemann surface. In this case, \((S,\beta )\) is called an origami pair and \(\mathrm{Aut}(S,\beta )\) is the group of conformal automorphisms \(\phi \) of S such that \(\beta =\beta \circ \phi \).

Let \(\mathcal {S}\) be a nonempty semigroup endowed with a binary associative operation \(*\). An element e of \(\mathcal {S}\) is said to be idempotent if \(e*e=e\). Originated by one question of P. Erdős to D.A. Burgess: If \(\mathcal {S}\) is a finite semigroup of order n, does any \(\mathcal {S}\)-valued sequence T of length n contain a nonempty subsequence the product of whose terms, in some

We show that every solvable group is a subgroup of some monomial real group. This extends a result of Dade, who proved that every solvable group is a subgroup of a monomial group.

In this paper, we first prove the local existence of strong solutions to the 3D Boussinesq equations in a bounded domain with Navier boundary conditions. Then we show the global stability of strong large solutions under a suitable integral condition.

In a commutative ring R with unity, a unit u is called exceptional if \(u-1\) is also a unit. For \(R = {\mathbb {Z}}/n{\mathbb {Z}}\) and for any \(f(X) \in {\mathbb {Z}}[X]\), an element \({\overline{u}} \in {\mathbb {Z}}/n{\mathbb {Z}}\) is called an “f-exunit” if \(gcd(f(u),n) = 1\). Recently, we obtained the number of representations of a non-zero element of \({\mathbb {Z}}/n{\mathbb {Z}}\) as

We establish uniqueness results for quasilinear elliptic problems through the criterion recently provided in Bonheure et al. (Trans Amer Math Soc 370(10):7081–7127, 2018). We apply it to generalized p-Laplacian subhomogeneous problems that may admit multiple nontrivial nonnegative solutions. Based on a generalized hidden convexity result, we show that uniqueness holds among strongly positive solutions

In this article, we prove an isoperimetric inequality for the harmonic mean of the first \((n-1)\) nonzero Steklov eigenvalues on bounded domains in n-dimensional hyperbolic space. Our approach to prove this result also gives a similar inequality for the first n nonzero Steklov eigenvalues on bounded domains in n-dimensional Euclidean space.

The Liouville–von Neumann equation describes the change in the density matrix with time. Interestingly, this equation was recently regarded as a wave equation for wave functions but not as an equation for density functions. This setting leads to an extended form of the Schrödinger wave equation governing the motion of a quantum particle. In this paper, we obtain the integrability of the wave propagator

In this paper, we mainly investigate the conjugation of the sylowizer that was introduced by Gaschütz (Math Z 122(4):319–320, 1971) and study the p-supersolvability of finite groups by analyzing the intersection between \(O^{p}(G)\) and sylowizers of p-subgroups. As a continuation of research (Lei and Li in Arch Math (Basel) 114:367–376, 2020), we also give some characterizations on p-nilpotent groups

We estimate the size of the singular set on \(\partial {\mathbb {B}}\) where a positive superharmonic function satisfying a nonlinear inequality like \(-\Delta u\le c u^p\) in the unit ball \({\mathbb {B}}\subset {\mathbb {R}}^n\) blows up faster than a prescribed order.

Let \(\mu _{M, D}\) be the self-affine measure generated by an expanding integer matrix \(M\in M_{2}(\mathbb {Z})\) and an integer three-element digit set \(D=\{(0,0)^T, (\alpha ,\beta )^T,(\gamma ,\eta )^T\}\). In this paper, we show that if \(3\mid \det (M)\) and \(3\not \mid \alpha \eta -\beta \gamma \), then \(L^2(\mu _{M,D})\) has an orthogonal basis of exponential functions if and only if \(M^*\varvec{u}\in

In this paper, we show that any topological knot or link in \(S^1 \times S^2\) sits on a planar page of an open book decomposition whose monodromy is a product of positive Dehn twists. As a consequence, any knot or link type in \(S^1 \times S^2\) has a Legendrian representative having support genus zero. We also show this holds for some knots and links in the lens spaces L(p, 1).

Let V be a non-trivial finite-dimensional vector space over a finite field F of characteristic p and let G be an irreducible subgroup of \(GL(V)\) having nilpotence class at most two. We prove that if \(|G|> |V|/2\), then G is cyclic, or \(|V|=3^2\) or \(5^2\). This is a refinement of Glauberman’s result for the tight bound of linear groups of nilpotence class two.

Motivated by the generalized Bloch conjecture, we formulate a conjecture about the Chow groups of Plücker hypersurfaces in Grassmannians. We prove weak versions of this conjecture.

In this paper, using a generalization of the notion of Prym variety for covers of projective varieties, we prove a structure theorem for the Mordell–Weil group of abelian varieties over function fields that are twists of abelian varieties by Galois covers of smooth projective varieties. In particular, the results we obtain contribute to the construction of Jacobians of high rank.

The aim of this paper is to give a complementary upper bound-type isoperimetric inequality for the fundamental Dirichlet eigenvalue of a bounded domain completely contained in a cone. This inequality is a counterpart to the Ratzkin inequality for Euclidean wedge domains in higher dimensions. We also give a new version of the Crooke–Sperb inequality involving a new geometric quantity for the first eigenfunction

We investigate branched regular finite abelian A-covers of the 2-sphere, where every homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface. In this study, we prove that if A is a finite abelian p-group of rank k and \(\Sigma \rightarrow S^2\) is a regular A-covering branched over n points such that every homeomorphism \(f:S^2 \rightarrow S^2\) lifts

It is shown that a connected Riemannian manifold has constant sectional curvature if and only if every one of its points is a non-degenerate maximum of some germ of smooth functions whose Riemannian gradient is a conformal vector field.

We prove a theorem, which generalises C. Franchetti’s estimate for the norm of a projection onto a rich subspace of \(L^p([0, 1])\) and the authors’ related estimate for compact operators on \(L^p([0, 1])\), \(1 \le p < \infty \).

Let \(p \geqslant 3\) be a prime number and let \(n \geqslant 0\) be an integer such that \(p-1\) divides n. In this short note, we construct a family of (p, n)-gonal Riemann surfaces of maximal genus \(2np+(p-1)^2\) with more than one (p, n)-gonal group.

Given two primes p and q, we study degrees and rationality of irreducible characters in the principal p-block of \({\mathfrak {S}}_n\) and \({\mathfrak {A}}_n\), the symmetric and alternating groups. In particular, we show that such a block always admits an irreducible character of degree divisible by q. This extends and generalizes a recent result of Giannelli–Malle–Vallejo.

In recent papers, the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the twice continuous differentiability of its generator. As a consequence of this result, we can characterize those quasiarithmetic means which admit a lower convex and upper

In the setting of bounded strongly Lipschitz domains, we present a short and simple proof of the compactness of the trace operator acting on square integrable vector fields with square integrable divergence and curl with a boundary condition. We rely on earlier trace estimates established in a similar setting.

In this work, we analyze a truncated version for the Timoshenko beam model with thermal and mass diffusion effects derived by Aouadi et al. (Z Angew Math Phys 70:117, 2019). In particular, we study some issues related to the second spectrum of frequency according to a procedure due to Elishakoff (in: Advances in mathematical modelling and experimental methods for materials and structures, solid mechanics

In recent work, we use Dudek’s method together with a result of Zagier to establish an asymptotic formula for the average number of divisors of an irreducible quadratic polynomial of the form \(x^{2}-bx+c\) with b, c integers. In this note, we remark that one can adopt the work of Hooley to derive a more precise asymptotic formula for the case \(x^{2}-bx+c\) with \(b^{2}-4c\) not a square, and as a

We work with a conjecture on the BNS-invariant of Artin groups stated by Almeida and Kochloukova. We show that the class of Artin groups that satisfy this conjecture is closed under finite graph products. As a consequence, we show that the conjecture is true for all Artin groups of finite type and other subclasses.

In this paper, we study when a composition operator or a weighted composition operator on a Banach space of holomorphic functions is a Ritt operator or an unconditional Ritt operator. It turns out that for composition operators or weighted composition operators on a Banach space of holomorphic functions, if a composition operator or a weighted composition operator is a Ritt operator, then it is also

In this work, it is shown that for the classical Cartan domain \(\mathcal {R}_{II}\) consisting of symmetric \(2\times 2\) matrices, every algebraic subset of \(\mathcal {R}_{II}\), which admits the polynomial extension property, is a holomorphic retract.

By a length-preserving flow, we provide a new proof of a conjecture on the reverse isoperimetric inequality composed by Pan et al. (Math Inequal Appl 13:329–338, 2010), which states that if \(\gamma \) is a convex curve with length L and enclosed area A, then the best constant \(\varepsilon \) in the inequality $$\begin{aligned} L^2\le 4\pi A+\varepsilon |{\tilde{A}}| \end{aligned}$$ is \(\pi \), where

We show that if a link J in the 3-sphere is homotopy ribbon concordant to a link L, then the Alexander polynomial of L divides the Alexander polynomial of J.

Let G be a finite primitive permutation group on a set \(\Omega \) with non-trivial point stabilizer \(G_{\alpha }\). We say that G is extremely primitive if \(G_{\alpha }\) acts primitively on each of its orbits in \(\Omega {\setminus } \{\alpha \}\). In earlier work, Mann, Praeger, and Seress have proved that every extremely primitive group is either almost simple or of affine type and they have

We prove a change of base theorem for operator space modules over C*-algebras, analogous to the change of rings for algebraic modules. We demonstrate how this can be used to show that the category of (right) matrix normed modules and completely bounded module maps has enough injectives.

If \(\psi :[0,\ell ]\rightarrow [0,\infty [\) is absolutely continuous, nondecreasing, and such that \(\psi (\ell )>\psi (0)\), \(\psi (t)>0\) for \(t>0\), then for \(f\in L^1(0,\ell )\), we have $$\begin{aligned} \Vert f\Vert _{1,\psi ,(0,\ell )}:=\int \limits _0^\ell \frac{\psi '(t)}{\psi (t)^2}\int \limits _0^tf^*(s)\psi (s)dsdt\approx \int \limits _0^\ell |f(x)|dx=:\Vert f\Vert _{L^1(0,\ell )}

We show that two-dimensional conformally related Douglas metrics are Randers.

We prove that the projectivized cotangent bundles of smooth quadrics of dimensions three and four are \((p-1)\)-th Frobenius split when \(p>10\). Besides, we show that the cotangent bundles of certain ordinary elliptic K3 surfaces are not Frobenius split.

In this note, we introduce a criterion to detect vanishing of essential algebras of a Green biset functor by means of morphisms. We introduce the inflation morphism and restriction morphism to prove that the essential supports of a Green biset functor and its shifted functors are the same. We use the kernel of the restriction to give a characterization of the seeds of the shifted functors.

Two subgroups A and B of a group G are called msp-permutable if the following statements hold: AB is a subgroup of G; the subgroups P and Q are mutually permutable, where P is an arbitrary Sylow p-subgroup of A and Q is an arbitrary Sylow q-subgroup of B, \({p\ne q}\). In the present paper, we investigate groups that are factorized by two msp-permutable subgroups. In particular, the supersolubility

We prove that horospheres, hyperspheres, and hyperplanes in a hyperbolic space \({\mathbb {H}}^n,\,n\ge 3\), admit no perturbations with compact support which increase their mean curvature. This is an extension of the analogous result in the Euclidean spaces, due to M. Gromov, which states that a hyperplane in a Euclidean space \({\mathbb {R}}^n\) admits no mean convex perturbations with compact supports

Let G be the alternating group \({{\,\mathrm{Alt}\,}}(n)\) on n letters. We prove that for any \(\varepsilon > 0\), there exists \(N = N(\varepsilon ) \in \mathbb {N}\) such that whenever \(n \ge N\) and A, B, C, D are normal subsets of G each of size at least \(|G|^{1/2+\varepsilon }\), then \(ABCD = G\).

In this paper, we study the following nonlinear elliptic systems: $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u_1+V_1(x)u_1=\partial _{u_1}F(x,u)&{}\quad x\in {\mathbb {R}}^N,\\ -\Delta u_2+V_2(x)u_2=\partial _{u_2}F(x,u)&{}\quad x\in {\mathbb {R}}^N, \end{array}\right. } \end{aligned}$$ where \(u=(u_1,u_2):{\mathbb {R}}^N\rightarrow {\mathbb {R}}^2\), F and \(V_i\) are periodic in \(x_1,\ldots

Recently, Araya, Celikbas, Sadeghi, and Takahashi proved a theorem about the vanishing of self extensions of finitely generated modules over commutative Noetherian rings. The aim of this paper is to obtain extensions of their result over algebras.

We characterize spheres as the unique complete properly immersed self-shrinkers in arbitrary codimension satisfying a geometric inequality.

We consider the Fano scheme \(F_k(X)\) of k-dimensional linear subspaces contained in a complete intersection \(X \subset {\mathbb {P}}^n\) of multi-degree \({\underline{d}} = (d_1, \ldots , d_s)\). Our main result is an extension of a result of Riedl and Yang concerning Fano schemes of lines on very general hypersurfaces: we consider the case when X is a very general complete intersection and \(\Pi

We investigate the class number one problem for a parametric family of real quadratic fields of the form \(\mathbb {Q}( \sqrt{m^2+4r})\) for certain positive integers m and r.

In this paper, we use the Fourier–Hermite functionals to extend the structure of the Cameron–Martin translation theorem on an abstract Wiener space \((H,B,\nu )\). The directional function in our translation theorem may not be in the Cameron–Martin subspace H of B. We then proceed to obtain an explicit formula for our general translation theorem.

The cover-avoidance property and its variations have become central in the study of finite groups. Along with this widespread attention comes a need to construct examples and counterexamples. The main goal of this work is to apply the theory of direct products to systematically facilitate such constructions.

In this paper, we consider the following conjecture, proposed by Brian Alspach, concerning partial sums in finite cyclic groups: given a subset A of \(\mathbb {Z}_n{\setminus } \{0\}\) of size k such that \(\sum _{z\in A} z\not = 0\), it is possible to find an ordering \((a_1,\ldots ,a_k)\) of the elements of A such that the partial sums \(s_i=\sum _{j=1}^i a_j\), \(i=1,\ldots ,k\), are nonzero and

For arbitrary \(S^{1}\)-actions on \(S^{m}_{{\mathbb {Q}}}\), \(S^{n}_{{\mathbb {Q}}}\), and \(S^{m}_{{\mathbb {Q}}}\times S^{n}_{{\mathbb {Q}}}\), we show the conditions for the tenability of the homotopy equivalence \((S^{m}_{{\mathbb {Q}}})^{hS^{1}}\times (S^{n}_{{\mathbb {Q}}})^{hS^{1}}\simeq (S^{m}_{{\mathbb {Q}}}\times S^{n}_{{\mathbb {Q}}})^{hS^{1}}\). Here, \(X^{hS^1}\) denotes the homotopy

Using the sub-supersolution method, we study the existence of positive solutions for the anisotropic problem $$\begin{aligned} -\sum _{i=1}^N\frac{\partial }{\partial x_i}\left( \left| \frac{\partial u}{\partial x_i}\right| ^{p_i-2}\frac{\partial u}{\partial x_i}\right) =\lambda u^{q-1} \end{aligned}$$(0.1) where \(\Omega \) is a bounded and regular domain of \({\mathbb {R}}^N\), \(q>1\), and \(\lambda

Let G be a finite soluble group and \(G^{(k)}\) the kth term of the derived series of G. We prove that \(G^{(k)}\) is nilpotent if and only if \(|ab|=|a||b|\) for any \(\delta _k\)-values \(a,b\in G\) of coprime orders. In the course of the proof, we establish the following result of independent interest: let P be a Sylow p-subgroup of G. Then \(P\cap G^{(k)}\) is generated by \(\delta _k\)-values

In this short note, studying 3-dimensional compact and minimal submanifolds of the \((3+p)\)-dimensional unit sphere \({\mathbb {S}}^{3+p}(1)\), we establish two rigidity theorems in terms of the Ricci curvature. The first theorem related to hypersurfaces of \({\mathbb {S}}^4(1)\) gives a new characterization of the minimal Clifford torus, whereas the second theorem is about the Legendrian submanifolds

Let \({\mathcal {C}}({\mathcal {H}})={\mathcal {B}}({\mathcal {H}})/{\mathcal {K}}({\mathcal {H}})\) be the Calkin algebra (\({\mathcal {B}}({\mathcal {H}})\) the algebra of bounded operators on the Hilbert space \({\mathcal {H}}\), \({\mathcal {K}}({\mathcal {H}})\) the ideal of compact operators, and \(\pi :{\mathcal {B}}({\mathcal {H}})\rightarrow {\mathcal {C}}({\mathcal {H}})\) the quotient map)

Using the recent work of Bettiol, we show that a first-order conformal deformation of Wilking’s metric of almost-positive sectional curvature on \(S^2\times S^3\) yields a family of metrics with strictly positive average of sectional curvatures of any pair of 2-planes that are separated by a minimal distance in the 2-Grassmanian. A result of Smale allows us to conclude that every closed simply connected