Related papers: A note on a metric associated to certain finite gr…
We consider groups of finite Morley rank with solvable local subgroups of even and mixed types. We also consider miscellaneous aspects of small groups of finite Morley rank of odd type.
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu
We classify the matrices M which correspond to finite categories
In this paper we classify the finite groups satisfying the following property $P_4$: their orders of representatives are set-wise relatively prime for any 4 distinct non-central conjugacy classes.
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…
A finite group $G$ is said to be a $\mathcal{B}_{\psi}$-group if $\psi(H)<|G|$ for any proper subgroup $H$ of $G$, where $\psi(H)$ denotes the sum of element orders of $H$. In this paper, we characterize the $\mathcal{B}_{\psi}$-groups up…
We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \otimes y= 1_{_{G \otimes G}}$ in the nonabelian tensor square $G \otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has…
In this note, we show that among finite nilpotent groups of a given order or finite groups of a given odd order, the cyclic group of that order has the minimum number of edges in its cyclic subgroup graph. We also conjecture that this holds…
We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.
In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.
In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.
We introduce the metric space valued in partially ordered groups, and define the convergence of sequences and the multi-valued weak contractions, etc., on the space. We then establish endpoint theorems for the defined maps. Our…
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…
We describe a perfect group whose localization is not perfect.
We focus on working on incidence rings, a class of (possibly infinite) matrix rings indexed by ordered sets. Some general properties about them are given, including how they are always the inverse limit of finite matrix rings, giving a…
In this paper we introduce and study the concept of normality degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be normal. Explicit formulas are obtained for some particular classes of…