Affine surfaces with finite fundamental group at infinity I: Bounds on second Betti number

Local–global generation property of commutators in finite π-soluble groups

Abstract We study the stationary properties of interacting ultracold bosons in a small one dimensional (1D) ring-shaped lattices within a Bose-Hubbard model using finite density matrix renormalization group (fDMRG). Small system size highlights the impact of the periodic boundary condition on the phase transition boundaries and the density-density correlation. Heat maps, as a function of chemical potential and hopping coupling, of differential expectations with respect to the ground and the excited states of energy, entropy and particle number, display a oscillatory stripe pattern that follow the trend of the phase boundaries. These features progressively diminish with system size, and are qualitatively independent of the boundary condition. A mean field analysis demonstrates that the striping is a finite size effect. The momentum distribution as a function of a phase on the hopping potential displays flux quantization effects of the non-trivial topology.

Iterated Finite Group Actions on Closed Connected Aspherical Manifolds

Abstract Random walks in a finite Abelian group G are studied. They use Markov chains with doubly stochastic transition matrices, in a Birkhoff subpolytope B ( G ) associated with the group G . It is shown that all future probability vectors belong to a polytope which does not depend on the transition matrices, and which shrinks during time evolution. Various quantities are used to describe the probability vectors: the majorization preorder, Lorenz values and the Gini index, entropic quantities, and the total variation distance. The general results are applied to the additive group Z ( d ) , and to the Heisenberg–Weyl group H W ( d ) / Z ( d ) . A physical implementation of random walks in Z ( d ) that involves a sequence of non-selective projective measurements, is discussed. A physical implementation of random walks in the Heisenberg–Weyl group H W ( d ) / Z ( d ) using a sequence of non-selective positive operator-valued measure measurements with coherent states, is also presented.

Abstract We provide the foundation of the spectral analysis of the Laplacian on the orbital Schreier graphs of the Basilica group, the iterated monodromy group of the quadratic polynomial $z^{2}-1$. This group is an important example in the class of self-similar amenable but not elementary amenable finite automata groups studied by Grigorchuk, żuk, Šunić, Bartholdi, Virág, Nekrashevych, Kaimanovich, and Nagnibeda et al. We prove that the spectrum of the Laplacian has infinitely many gaps and that the support of the Kesten--von-Neumann--Serre (KNS) Spectral Measure is a Cantor set. Moreover, on a generic blowup, the spectrum coincides with this Cantor set, and is pure point with localized eigenfunctions and eigenvalues located at the endpoints of the gaps.

A subgroup S of a finite group G is called a p-sylowizer of a p-subgroup R in G if S is maximal in G with respect to having R as its Sylow p-subgroup. A subgroup A of a finite group G is called a p-CAP-subgroup of G if it covers or avoids every p-chief factor of G, and A is called a strong p-CAP-subgroup of G if for any subgroup H of G containing A, A is a p-CAP-subgroup of H. We use the concepts of p-sylowizers and (strong) p-CAP-subgroups to obtain new criteria for p F -hypercentral embedding of normal subgroups.

Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. Many research works have revealed that certain properties of the maximal invariant subgroups under a coprime action may provide relevant information on the invariant structure of a group. In this paper, we study the structure of a group in which every maximal A-invariant subgroup of its Sylow p-subgroups is ρ -semipermutable and some new results are obtained.

A subgroup H of a finite group G is said to be a semi cover-avoiding subgroup of G if there is a normal series of G such that H covers or avoids every normal factor of the series. In this paper, we establish new criteria for the solvability and p-nilpotency of finite groups by analyzing semi cover-avoiding subgroups in the setting of coprime actions. Our results extend and generalize several recent results in the literature.

We show that parabolic Kazhdan–Lusztig polynomials of type A compute the decomposition numbers in certain Harish-Chandra series of unipotent characters of finite groups of Lie types B , C , and D over a field of non-defining odd characteristic \ell . Here, \ell is a “unitary prime” – the case that remains open in general, in the sense that it cannot be reduced to a similar problem for q -Schur algebras. The bipartitions labeling the characters in these series are small with respect to d , the order of q \bmod \ell , although they occur in blocks of arbitrarily high defect. Our main technical tool is the categorical action of an affine Lie algebra on the category of unipotent representations, which identifies the branching graph for Harish-Chandra induction with the \widehat{\mathfrak{sl}}_{d} -crystal on a sum of level 2 Fock spaces. Further key combinatorics has been adapted from Brundan and Stroppel’s work on Khovanov arc algebras to obtain the closed formula for the decomposition numbers in a d -small Harish-Chandra series.

Finite groups with maximum vertex degree commuting graphs

Finite groups in which every irreducible character has either p′-degree or p′-codegree

Online First 2026 UDK 512.542 MSC: 20D60, 05C25 DOI: 10.21538/0134-4889-2026-32-1-fon-03 The work is supported by Russian Science Foundation, project 24-11-00119, https://rscf.ru/en/project/24-11-00119/ Dedicated to the bright memory of Professor Otto Helmut Kegel The spectrum of a finite group G is the set of all element orders of G. The Gruenberg—Kegel graph (or the prime

A central limit theorem on two-sided descents of Mallows distributed elements of finite Coxeter groups

Block-transitive t-(k2,k,λ) designs and finite simple exceptional groups of Lie type

The quasi-polynomiality of mod q permutation representations for a linear finite group action on a lattice

A generalized character related to the p-local structure and representation theory of a finite group

In this paper, we show that all Coleman automorphisms of wreath products of some finite groups with trivial centers by any finite group are inner. In particular, the normalizer property holds for these groups.

Let G be a finite group. The vertex set of the prime-power graph of G is defined as V(G)=pep(G)|p∈ρ(G), where ρ(G) is the set of all prime divisors of the degrees of all irreducible characters of G and pep(G)=maxψ(1)p∣ψ∈Irr(G). It has been proved that the simple groups L3(p) can be characterized by its orders and vertex set of prime-power graphs. In this paper, we continue this topic and prove that L3(p2) can be uniquely characterized by its orders and degree prime-power graphs, where p is a prime.

Abstract Let G be a finite, non-cyclic, non-characteristically simple group, such that all its proper characteristic subgroups are cyclic. We call such a group a $$\textrm{CCS}$$ CCS group, short for Characteristic Cyclic Subgroups . In this paper, we provide a complete classification of these groups. As a consequence, we obtain an alternative proof that any skew brace whose multiplicative group is cyclic of p -power order, with p an odd prime, necessarily has a cyclic additive group. Moreover, we describe the multiplicative group of skew braces whose additive group is a solvable, non-nilpotent $$\textrm{CCS}$$ CCS group.