Related papers: Existence criterion for Hall subgroups of finite g…
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
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 $G$.
Let $G$ be a finite group, and let $\pi$ be a set of primes. The aim of this paper is to obtain some results concerning how much information about the $\pi$-structure of $G$ can be gathered from the knowledge of the lengths of conjugacy…
Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.
A criterion for the HNN-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HNN-extension with arbitrary base group is proved.…
In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.
The principle result of this article is the determination of the possible finite subgroups of arithmetic lattices in U(2,1).
Given a group satisfying sufficient finiteness properties, we discuss a group algebra criterion for vanishing of all its cohomology groups with unitary coefficients in a certain degree.
We prove a $p$-nilpotency criterion for finite groups in terms of the element orders of its $p'$-reduced sections that extends a nilpotency criterion by T{\u{a}}rn{\u{a}}uceanu.
We show the existence of Hall polynomials for representation-finite cluster-tilted algebras.
We show that under certain conditions the Gelfand-Kazhdan criterion for the Gelfand property is a necessary condition. We work in the generality of finite groups, however part of the argument carries over to p-adic and real groups.
In the present paper, the structure of a finite group $G$ having a nonnormal T.I. subgroup $H$ which is also a Hall $\pi$-subgroup is studied. As a generalization of a result due to Gow, we prove that $H$ is a Frobenius complement whenever…
In this paper we obtain significant bounds for the number of maximal subgroups of a given index of a finite group. These results allow us to give new bounds for the number of random generators needed to generate a finite $d$-generated group…
An upper bound of composition series of groups of finite order is obtained. The bound is a nontrivial bound and so far best possible.
In this note we determine the finite groups that can be written as the union of any three irredundant/distinct proper subgroups. The finite groups that can uniquely be written as the union of three proper subgroups are also characterized.
We introduce a necessary and sufficient criterion for determining the existence and the values of ratio limits of complex sequences generated by arbitrary linear recurrences.
Let $H$ be a subgroup of a group $G$. We say that $H$ satisfies the power condition with respect to $G$, or $H$ is a power subgroup of $G$, if there exists a non-negative integer $m$ such that $H=G^{m}=<g^{m} | g \in G >$. In this note, the…
The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.
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 establish conditions under which the fundamental group of a graph of finite $p$-groups is necessarily residually $p$-finite. The technique of proof is independent of previously established results of this type, and the result is also…