Related papers: A note on localizations of perfect groups

Let $d \geq 2$ be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite $d$-generated perfect groups. We prove a special case of this conjecture for the finite perfect groups…

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…

Every locally compact local group is locally isomorphic to a topological group.

A countable group G is called k-linear sofic (for some 0 <k \le 1) if finite subsets of G admit "approximate representations" by complex invertible matrices in the normalized rank metric, so that non-identity elements are k-away from the…

We introduce and study varions notions of completeness of translation-invariant ideals in groups.

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

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 note we answer a question concerning lineability of the set of non-absolutely summing operators.

We establish a necessary and sufficient condition for a normal subgroup of a finite group to be a subgroup perfect code.

In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

We give new characterizations of sofic groups: -- A group $G$ is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups. -- A group $G$ is sofic if and only if any system of equations…

This paper investigates the critical group of a faithful representation of a finite group. It computes the order of the critical group in terms of the character values, and gives some restrictions on its subgroup structure. It also computes…

If $G$ is a finite group and $x\in G$ then the set of all elements of $G$ having the same order as $x$ is called {\em an order subset of $G$ determined by $x$} (see [2]). We say that $G$ is a {\em group with perfect order subsets} or…

In this short note we give various near optimal characterizations of random walks over finite Abelian groups with large maximum discrepancy from the uniform measure. We also provide several interesting connections to existing results in the…

In this paper, we study the parallelism between perfect numbers and Leinster groups and continue it by introducing the new concepts of almost and quasi Leinster groups which parallel almost and quasi perfect numbers. These are small…

We show that the closure of the compactly supported mapping class group of an infinite type surface is not perfect and that its abelianization contains a direct summand isomorphic to an uncountable direct sum of rationals. We also extend…

We construct examples of localizations in the category of groups which take the Mathieu group $M_{11}$ to groups of arbitrarily large cardinality which are ``abelian up to finitely many generators''. The paper is part of a broader study on…

Let $A \leq G$ be a subgroup of a group $G$. An $A$-complement of $G$ is a subgroup $H$ of $G$ such that $G = A H$ and $A \cap H = \{1\}$. The \emph{classifying complements problem} asks for the description and classification of all…