Related papers: A note on a metric associated to certain finite gr…
Let $G$ be a finite group. In this short note, we give a criterion of nilpotency of $G$ based on the existence of elements of certain order in each section of $G$.
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
In this paper we introduce and study the lattice of normal subgroups of a group $G$ that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of $G$ (see \cite{5}). A precise description of…
We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover…
In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.
In this short note, a bound on the word metric for Thompson's group V given by Birget in 2004 is improved to a new bound, which agrees with the known bounds for Thompson's groups F and T.
In the paper new criteria of existence and conjugacy of Hall subgroups of finite groups are given.
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.
The purpose of this note is twofold. In the first part we observe that two finitely generated non-amenable groups are quasi-isometric if and only if they admit topologically orbit equivalent Cantor minimal actions. In particular, free…
In this paper, we describe the structure of finite groups whose element orders or proper (abelian) subgroup orders form an arithmetic progression of ratio $r\geq 2$. This extends the case $r=1$ studied in previous papers \cite{1,8,4}.
In this note, we consider models in $\mathbb C^2$. The purpose of this note is twofold. We first show a characterization of models in $\mathbb C^2$ by their noncompact automorphism groups. Then we give an explicit description for…
We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.
In this expository article intended to be accessible to undergraduate students we introduce a finite abelian group that can be associated to any finite connected graph. This group can be defined in an elementary combinatorial way in terms…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…
In this preliminary note we prove that the theory of valued fields equipped with an action of a given finite group has a model companion.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones