Related papers: Finite metacyclic groups as active sums of cyclic …

We prove that the subgroup graph of a finite group $G$ is regular if and only if $G$ is cyclic with square-free order.

We define and we characterize regular and c-regular cyclically ordered abelian groups. We prove that every dense c-regular cyclically ordered abelian group is elementarily equivalent to some cyclically ordered group of unimodular complex…

We classify the factorizations of finite classical groups with nonsolvable factors, completing the classification of factorizations of finite almost simple groups.

Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…

A countable group is residually finite if every nontrivial element can act nontrivially on a finite set. When a group fails to be residually finite, we might want to measure how drastically it fails - it could be that only finitely many…

Pontryagin duality provides a powerful tool for analyzing the structure and properties of locally compact abelian groups, in particular finite abelian groups. Now much can be done with non-abelian groups via the construction of character…

We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.

This article continues a prior investigation of the authors with the goal of extending characterization results of convolutional tight frames from the context of cyclic groups to general finite abelian groups. The collections studied are…

We study Farrell Nil-groups associated to a finite order automorphism of a ring $R$. We show that any such Farrell Nil-group is either trivial, or infinitely generated (as an abelian group). Building on this first result, we then show that…

We define a cocycle on the group of symplectic diffeomorphisms of a symplectic manifold and investigate its properties. The main applications are concerned with symplectic actions of discrete groups. For example, we give an alternative…

In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.

We prove that if a finite group $G$ acts smoothly on a manifold $M$ so that all the isotropy subgroups are abelian groups with rank $\leq k$, then $G$ acts freely and smoothly on $M \times \bbS^{n_1} \times...\times \bbS^{n_k}$ for some…

We classify dynamical twists in group algebras of finite groups. Namely, we set up a bijective correspondence between gauge equivalence classes of dynamical twists (which are solutions of a certain non-linear functional equation) and…

In this paper it is shown that every finite cyclic group satisfies the CI-property for the class of balanced configurations.

We show that the free-by-cyclic groups of the form F(2)-by-Z act properly cocompactly on CAT(0) square complexes. We also show using generalised Baumslag-Solitar groups that all known groups defined by a 2-generator 1-relator presentation…

A group $G$ is called logically cyclic, if it contains an element $s$ such that every element of $G$ can be defined by a first order formula with parameter $s$. The aim of this paper is to investigate the structure of such groups.

We describe the structure of finite groups with $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups when $\mathfrak{F}$ is a subgroup-closed saturate superradical formation containing all nilpotent groups. We prove that…

We initiate the study of finite abelian groups that faithfully act on 3-dimensional rationally connected varieties. We show that these groups can be naturally divided into three types: the groups of product type are finite abelian groups…

We show that if G is an infinitely generated locally (polycyclic-by-finite) group with cohomology almost everywhere finitary, then every finite subgroup of G acts freely and orthogonally on some sphere.

The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups with abelian Sylow $2$-subgroups. For every positive integer…