Related papers: Finiteness results for subgroups of finite extensi…

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group…

We show that an infinite residually finite boundedly generated group has an infinite chain of finite index subgroups with ranks uniformly bounded, and give (sublinear) upper bounds on the ranks of arbitrary finite index subgroups of…

This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah,…

In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we classify finite semigroups such that the…

For a finite point set $E\subset \mathbb{R}^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k + 1$ points in E such that the distance between a pair of points is specified if the…

We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i) |N_G(H):H| is finite for every non-normal subgroup H of G, and (ii) |C_G(x):<x>| is finite for every non-normal cyclic subgroup <x> of G.…

We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively…

We show that doubling at some large scale in a Cayley graph implies uniform doubling at all subsequent scales. The proof is based on the structure theorem for approximate subgroups proved by Green, Tao and the first author. We also give a…

We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.

Using graph-theoretic techniques for f.g. subgroups of $F^{\mathbb{Z}[t]}$ we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked…

We describe the groups of inner and outer automorphisms of the free metabelian nilpotent Lie algebra of finite rank over a field of characteristic 0. To obtain this result we first describe the groups of inner and continuous outer…

We construct the first examples of finitely presented groups with cubic Dehn function containing a finitely generated infinite torsion subgroup. Moreover, we show that any infinite free Burnside group with sufficiently large odd exponent…

Let G be a simple Lie group of real rank one, and S the ideal boundary of the corresponding symmetric space of noncompact type (H^n_R, H^n_C, H^n_H or H^2_O). We show the finiteness of the possible values of the secondary characteristic…

In a recent paper Cameron, Lakshmanan and Ajith began an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a new perspective. Following their suggestions, we consider suitable…

In this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain "universal extension classes" for the general linear supergroup. Some of these classes restrict to the universal…

We prove an infinite Ramsey theorem for noncommutative graphs realized as unital self-adjoint subspaces of linear operators acting on an infinite dimensional Hilbert space. Specifically, we prove that if V is such a subspace, then provided…

We give criteria for a graph of groups to have finite stature with respect to its collection of vertex groups, in the sense of Huang-Wise. We apply it to the triangle Artin groups that were previously shown to split as a graph of groups.…

The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups…

We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose…

We derive a generating series for the number of free subgroups of finite index in $\Delta^+ = \mathbb{Z}_p*\mathbb{Z}_q$ by using a connection between free subgroups of $\Delta^+$ and certain hypermaps (also known as ribbon graphs or "fat"…