Related papers: Algebraic theory of abelian groups
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that…
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally…
We introduce two notions of algebraic entropy for actions of cancellative right amenable semigroups $S$ on discrete abelian groups $A$ by endomorphisms; these extend the classical algebraic entropy for endomorphisms of abelian groups,…
Ergodic theory, Higher order Fourier analysis and the hyper graph regularity method are three possible approaches to Szemer\'edi type theorems in abelian groups. In this paper we develop an algebraic theory that creates a connection between…
In this paper we study (logical) types and isotypical equivalence of torsion free Abelian groups. We describe all possible types of elements and standard 2-tuples of elements in these groups and classify separable torsion free Abelian…
In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…
We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…
A set of quasi-uniform random variables $X_1,...,X_n$ may be generated from a finite group $G$ and $n$ of its subgroups, with the corresponding entropic vector depending on the subgroup structure of $G$. It is known that the set of entropic…
A group element is called generalized torsion if a finite product of its conjugates is equal to the identity. We show that in a finitely generated abelian-by-finite group, an element is generalized torsion if and only if its image in the…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian subgroup. We show that all discrete subgroups of complex simply connected almost Abelian groups are finitely generated. The topology of connected almost…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
It is shown that every separable abelian topological group is isomorphic with a topological subgroup of a monothetic group (that is, a topological group with a single topological generator). In particular, every separable metrizable abelian…
In this note some properties of the sum of element orders of a finite abelian group are studied.
By Torelli topology the author understands aspects of the topology of surfaces (potentially) relevant to the study of Torelli groups. The present paper is devoted to a new approach to the results of W. Vautaw about Dehn multi-twists in…
We define the geometric simpleness for toroidal groups. We give an example of quasi-abelian variety which is geometrically simple, but not simple. We show that any quasi-abelian variety is isogenous to a product of geometrically simple…
Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…
This article is devoted to showing the product theorem for Bowen's topological entropy.
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…