Related papers: Finite groups isospectral to simple groups

We give a description of a finite group whose maximal subgroups possess only soluble proper subgroups, which implies the answer to the well-known question on composition factors of finite groups, whose second maximal subgroups are soluble.

Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.

A subgroup of a finite group is wide if each prime divisor of the group order divides the subgroup order. We obtain the description of finite soluble groups with no wide subgroups. We also prove that a finite soluble group with nilpotent…

In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.

In the paper it is proven that Carter subgroups of a finite group are conjugate. A complete classification of Carter subgroups in finite almost simple groups is also obtained.

We show that the category of symmetric spectra can be used as a model for global equivariant homotopy theory of finite groups.

A finite group is said to have "perfect order classes" if the number of elements of any given order is either zero or a divisor of the order of the group. The purpose of this note is to describe explicitly the finite Hamiltonian groups with…

We introduce the notion of the depth of a finite group $G$, defined as the minimal length of an unrefinable chain of subgroups from $G$ to the trivial subgroup. In this paper we investigate the depth of (non-abelian) finite simple groups.…

This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…

This paper studies intersections of principal blocks of a finite group with respect to different primes. We first define the block graph of a finite group $G$, whose vertices are the prime divisors of $|G|$ and there is an edge between two…

If $G$ is a finite group, then the spectrum $\omega(G)$ is the set of all element orders of $G$. The prime spectrum $\pi(G)$ is the set of all primes belonging to $\omega(G)$. A simple graph $\Gamma(G)$ whose vertex set is $\pi(G)$ and in…

In \cite[Problem 72]{Fuchs60} Fuchs asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases. The aim of…

This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.

A \emph{finite cover} of a group $G$ is a finite collection $\mathcal{C}$ of proper subgroups of $G$ with the property that $\bigcup \mathcal{C} = G$. A finite group admits a finite cover if and only if it is noncyclic. More generally, it…

In this paper, we explain the importance of finite decomposition semigroups and present two theorems related to their structure.

In this short note, we describe finite groups all of whose non-trivial cyclic subgroups have the same Chermak-Delgado measure.

This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…

A finite group $G$ is called *uniformly generated*, if whenever there is a (strictly ascending) chain of subgroups $1<\langle x_1\rangle<\langle x_1,x_2\rangle <\cdots<\langle x_1,x_2,\dots,x_d\rangle=G$, then $d$ is the minimal number of…

The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free…

For a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group,…