Related papers: On the Mackey problem for free abelian topological…

Following [23], denote by $\mathfrak{F}_0$ the functor on the category $\mathbf{TAG}$ of all Hausdorff Abelian topological groups and continuous homomorphisms which passes each $X\in \mathbf{TAG}$ to the group of all $X$-valued null…

Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. In this paper, we consider two topological properties of $F(X)$ or $A(X)$,…

We show that every finitely generated group G with an element of order at least $(5rank(G))^{12}$ admits a locally finite directed Cayley graph with automorphism group equal to G. If moreover G is not generalized dihedral, then the above…

In general a universal covering of a non connected topological group need not admit a topological group structure such that the covering map is a morphism of topological groups. This result is due to R.L. Taylor (1953). We generalise this…

Two (strongly) zero-dimensional Lindel\"of topological groups whose product has positive covering dimension are constructed. An example of a Lindel\"of (strongly) zero-dimensional space whose free and free Abelian topological groups are not…

We study topological versions of an independent set in an abelian group and a linearly independent set in a vector space, a {\em topologically independent set} in a topological group and a {\em topologically linearly independent set} in a…

We use the free entropy defined by D. Voiculescu to prove that the free group factors can not be decomposed as closed linear spans of noncommutative monomials in elements of nonprime subfactors or abelian $*$-subalgebras, if the degrees of…

This paper seeks to characterize some topological properties of pro-countable abelian topological groups. Using the Milnor exact sequence given by the controlled picture of $KK$-theory by Willett and Yu, we describe topological properties…

We extend results on transitive self-similar abelian subgroups of the group of automorphisms $\mathcal{A}_m$ of an $m$-ary tree $\mathcal{T}_m$ in \cite{BS}, to the general case where the permutation group induced on the first level of the…

We show that in general for a given group the structure of a maximal hyperbolic tower over a free group is not canonical: We construct examples of groups having hyperbolic tower structures over free subgroups which have arbitrarily large…

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…

We prove that if mu^+< lambda =cf(lambda)< mu^{aleph_0}, then there is no universal reduced torsion free abelian group. Similarly if aleph_0< lambda < 2^{aleph_0}. We also prove that if 2^{aleph_0}< mu^+< lambda =cf(lambda)< mu^{aleph_0},…

A natural topology on the set of left orderings on free abelian groups and free groups $F_n$, $n>1$ has studied in [1]. It has been proven already that in the abelian case the resulted topological space is a Cantor set. There was a…

For an abelian topological group G let G^* denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact abelian group G such that w(X) < w(G) and an open…

We prove the following group analogue of the well-known Heyde theorem on a characterization of the Gaussian distribution on the real line. Let $X$ be a second countable locally compact Abelian group containing no subgroups topologically…

We prove group existence and structure theorems in a general setting of tame topological theories. More precisely, we identify a linear/non-linear dividing line -- called topological 1-basedness -- among the class of t-minimal theories with…

For any left orderable group G, we recall from work of McCleary that isolated points in the space of left orderings correspond to basic elements in the free lattice ordered group over G. We then establish a new connection between the…

Let $A$ be an infinitely generated free abelian group. We prove that the automorphism group $\aut A$ first-order interprets the full second-order theory of the set $|A|$ with no structure. In particular, this implies that the automorphism…

A non-trivial topological group is called \emph{$d$-independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting it trivially. This notion was introduced by M\'arquez and…

For every $n \geq 1$, let $(\mathrm{FW}_n)$ denote the fixed-point property for median graphs of cubical dimension $n$ (or equivalently, for CAT(0) cube complexes of dimension $n$). In this article, we construct explicit examples of groups…