Related papers: Characterized subgroups of topological abelian gro…

A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has…

Let $G$ be a reductive group defined over a number field. Denote $Z(\hat G)$ the center of the dual group. Langlands has defined some homomorphism from some cohomology group of $Z(\hat G)$ into the group of automorphic characters of $G$. We…

The existence of a countably compact group without non-trivial convergent sequences in ZFC alone is a major open problem in topological group theory. We give a ZFC example of a Boolean topological group G without non-trivial convergent…

A space $X$ is of countable type (resp. subcountable type) if every compact subspace $F$ of $X$ is contained in a compact subspace $K$ that is of countable character (resp. countable pseudocharacter) in $X$. In this paper, we mainly show…

A topological group $G$ is {\em sequentially $h$-complete} if all the continuous homomorphic images of $G$ are sequentially complete. In this paper we give necessary and sufficient conditions on a complete group for being compact, using the…

We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…

Suppose $G$ is a finite group and $A\subseteq G$ is such that $\{gA:g\in G\}$ has VC-dimension strictly less than $k$. We find algebraically well-structured sets in $G$ which, up to a chosen $\epsilon>0$, describe the structure of $A$ and…

This paper is devoted to the study of the group ${\rm Ext} (G,H)$ of all extensions of topological abelian groups $0\to H\to X\to G\to 0$ and the group ${\rm Ext}_{TVS} (Z,Y)$ of all extensions of topological vector spaces $0\to Y\to X\to…

Let G be a simple non-compact linear connected Lie group and H be a closed non-compact semisimple subgroup. We are interested in finding classes of homogeneous spaces G/H admitting proper actions of discrete non virtually abelian subgroups…

The (reduced) characteristic group of a locally conformally product manifold is obtained by restricting the action of its fundamental group to the non-flat factor of the universal cover, and taking the connected component of the identity in…

It is proved that, in certain subgroups of direct products of countable groups, the property of being an unconditionally closed set coincides with that of being an algebraic set. In particular, these properties coincide in all Abelian…

We describe the supercharacter theories of the semidirect product of H and K, $H\rtimes K$ in terms of the supercharacter theories of the direct product of H and K in the case when both H and K are Abelian groups. To do this we introduce…

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…

Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable…

Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive…

We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.

We study locally compact groups having all subgroups minimal. We call such groups hereditarily minimal. In 1972 Prodanov proved that the infinite hereditarily minimal compact abelian groups are precisely the groups $\mathbb Z_p$ of $p$-adic…

We consider two variants of those Abelian groups with all proper strongly invariant subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…

We study locally compact groups having all dense subgroups (locally) minimal. We call such groups densely (locally) minimal. In 1972 Prodanov proved that the infinite compact abelian groups having all subgroups minimal are precisely the…

It is shown that each pseudonorm defined on a subgroup $H$ of an abelian group $G$ can be extended to a pseudonorm on $G$ such that the densities of the obtained pseudometrizable topological groups coincide. We derive from this that any…