Related papers: Finite direct sums of cyclic embeddings

Explicit embeddings of the group $\mathbb{Q}$ into a finitely presented group $\mathcal{Q}$ and into a $2$-generator finitely presented group $T_{\mathcal{Q}}$ are suggested. The constructed embeddings reflect questions mentioned by…

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.

It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism…

Presentations for the holomorphs of abelian groups of the form $C_{p^n} \times 1^{m}$ for $p$=2 or an odd prime are given. These presentations extend the results given in Burnside's well-known text on finite groups on the holomorphs for the…

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…

We give an algebraic description of the structure of the analytic universal cover of a complex abelian variety which suffices to determine the structure up to isomorphism. More generally, we classify the models of theories of "universal…

In this paper we consider the existence of dense embeddings of Limit groups in locally compact groups generalizing earlier work of Breuillard, Gelander, Souto and Storm [GBSS] where surface groups were considered. Our main results are…

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

The goal of this paper is to characterization generalized Alexander quandles of finite groups in the language of the underlying groups. Firstly, we prove that if finite groups $G$ are simple, then the quandle isomorphic classes of…

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group $\mathcal{M}_{\sigma}$ of a compact closed surface $X$ of genus $\sigma$ is considered. A complete method of enumeration is achieved for…

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even…

Groups of finite type (also called finitely constrained groups), introduced by Grigorchuk, are known to be the closure of regular branch groups. This article explores many of their properties. Firstly, we prove that being finitely…

For a finite group $G$, we define the inclusion graph of subgroups of $G$, denoted by $\mathcal I(G)$, is a graph having all the proper subgroups of $G$ as its vertices and two distinct vertices $H$ and $K$ in $\mathcal I(G)$ are adjacent…

To each algebra over the complex numbers we associate a sequence of abelian groups in a contravariant functorial way. In degree (m-1) we have the m-summable Fredholm modules over the algebra modulo stable m-summable perturbations. These new…

In this article we complete the work of enumerating typical abelian coverings of Cayley graphs, by reducing the problem to enumerating certain subgroups of finite abelian groups.

We study abelian varieties and K3 surfaces with complex multiplication defined over number fields of fixed degree. We show that these varieties fall into finitely many isomorphism classes over an algebraic closure of the field of rational…

We show that the \s{\phi}-labeled Thompson groups and the twisted Brin--Thompson groups are boundedly acyclic. This allows us to prove several new embedding results for groups. First, every group of type $F_n$ embeds quasi-isometrically…

We study the topological full group of ample groupoids over locally compact spaces. We extend Matui's definition of the topological full group from the compact, to the locally compact case. We provide two general classes of groupoids for…

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…