Related papers: Characterized subgroups of topological abelian gro…

We prove that if $H$ is a topological group such that all closed subgroups of $H$ are separable, then the product $G\times H$ has the same property for every separable compact group $G$. Let $c$ be the cardinality of the continuum. Assuming…

This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated…

We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact…

Let $L_1$ and $L_2$ be linear forms of real-valued independent random variables. By Heyde's theorem, if the conditional distribution of $L_2$ given $L_1$ is symmetric, then the random variables are Gaussian. A number of papers are devoted…

Let $X$ be a locally compact Abelian group with the connected component of zero of dimension 1. Let $\xi_1$ and $\xi_2$ be independent random variables with values in $X$ with nonvanishing characteristic functions. We prove that if a…

A group G is a cn-group if for each subgroup H of G there exists a normal subgroup N of G such that the index of both H and N in HN is finite. The class of cn-groups contains properly the classes of core- finite groups and that of groups in…

For any topological group $G$ the dual object $\hat G$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat G$ is discrete, and we investigate…

Let $H$ be an abelian subgroup of a finite group $G$ and $\pi$ the set of prime divisors of $|H|$. We prove that $|H O_{\pi}(G)/ O_{\pi}(G)|$ is bounded above by the largest character degree of $G$. A similar result is obtained when $H$ is…

We classify the unipotent character sheaves on a fixed connected component of a reductive algebraic group under a mild hypothesis on the characteristic of the ground field.

A topological group $X$ is defined to have $compact$ $exponent$ if for some number $n\in\mathbb N$ the set $\{x^n:x\in X\}$ has compact closure in $X$. Any such number $n$ will be called a compact exponent of $X$. Our principal result…

We study definably compact definably connected groups definable in a sufficiently saturated real closed field $R$. We introduce the notion of group-generic point for $\bigvee$-definable groups and show the existence of group-generic points…

We provide a systematic description of the automorphism groups of specially cocompact CAT(0) cube complexes. We show that these groups are topologically finitely generated, present a method to explicitly obtain generating sets, and prove a…

In a stable abelian group, we characterize generic types of cosets of type-definable subgroups.

In this paper, the characterization of domains in $\mathbb C^n$ by their noncompact automorphism groups are given.

Let $X$ be a locally compact Abelian group, $Y$ be its character group. Following A. Kagan and G. Sz\'ekely we introduce a notion of $Q$-independence for random variables with values in $X$. We prove group analogues of the Cram\'er,…

We perform a general study of the structure of locally compact modules over compactly generated abelian groups. We obtain a devissage result for such modules of the form "compact-by-sheer-by-discrete", and then study more specifically the…

Let $\{G_i :i\in\N\}$ be a family of finite Abelian groups. We say that a subgroup $G\leq \prod\limits_{i\in \N}G_i$ is \emph{order controllable} if for every $i\in \mathbb{N}$ there is $n_i\in \mathbb{N}$ such that for each $c\in G$, there…

We consider the question: When do two finite abelian groups have isomorphic lattices of characteristic subgroups? An explicit description of the characteristic subgroups of such groups enables us to give a complete answer to this question…

The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of…

The study of actions of countable groups by automorphisms of compact abelian groups has recently undergone intensive development, revealing deep connections with operator algebras and other areas. The discrete Heisenberg group is the…