Related papers: On t-extensions of abelian groups

In this paper, we study the group Pext(C,A) for locally compact abelian (LCA) groups A and C. Sufficient conditions are established for Pext(C,A) to coincide with the first Ulm subgroup of Ext(C,A). Some structural information on pure…

Let $X$ be a compact torsion abelian group. In this paper, we show that an extension of $F_{p}$ by $X$ splits where $F_{p}$ is the p-adic number group and $p$ a prime number. Also, we show that an extension of a torsion-free, non-divisible…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

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…

We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that: (1) A precompact Abelian group G of bounded order is reflexive iff the…

We prove a conjecture due to Baumgaertel and Lledo according to which for every compact group G one has Z(G)^ \cong C(G), where the `chain group' C(G) is the free abelian group (written multiplicatively) generated by the set G^ of…

In this paper, we show that for every locally compact abelian group G, the following statements are equivalent: (i) G contains no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0; (ii)…

Generalizing results from \cite{DTk,DU} we study the fine structure of locally minimal (locally) precompact Abelian groups (these are the locally essential subgroups $G$ of LCA groups $L$, i.e., such that $G$ non-trivially meets all…

Let $\ell$ be the category of all locally compact abelian (LCA) groups. Let $G\in\ell$ and $H\subseteq G$. The first Ulm subgroup of $G$ is denoted by $G^{(1)}$ and the closure of $H$ by $\overline{H}$. A proper short exact sequence $0\to…

To a compact Lie group $G$ one can associate a space $E(2,G)$ akin to the poset of cosets of abelian subgroups of a discrete group. The space $E(2,G)$ was introduced by Adem, F. Cohen and Torres-Giese, and subsequently studied by Adem and…

Assume V=L and lambda is regular smaller than the first weakly compact cardinal. Under those circumstances and with arbitrary requirements on the structure of Ext(G,Z) (under well known limitations), we construct an abelian group G of…

In this paper we complete the characterization of Ext(G,Z) under Godel's axiom of constructibility for any torsion-free abelian group G . In particular, we prove in (V=L) that, for a singular cardinal nu of uncountable cofinality which is…

Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic…

This paper opens and discusses the question originally due to Daniel Herden, who asked for which graph $(\mu,R)$ we can find a family $\{\mathbb G_\alpha: \alpha < \mu\}$ of abelian groups such that for each $\alpha,\beta\in\mu$:…

Peterzil and Steinhorn proved that if a group $G$ definable in an $o$-minimal structure is not definably compact, then $G$ contains a definable torsion-free subgroup of dimension one. We prove here a $p$-adic analogue of the…

In this paper, we study precompact abelian groups G that contain no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0. We characterize groups with this property in the following classes…

We present a series of examples of nondiscrete reflexive P-groups (i.e., groups in which all $G_\delta$-sets are open) as well as noncompact reflexive $\omega$-bounded groups (in which the closure of every countable set is compact). Our…

Let $G$ be a finite abelian group, and let $\eta(G)$ be the smallest integer $d$ such that every sequence over $G$ of length at least $d$ contains a zero-sum subsequence $T$ with length $|T|\in [1,\exp(G)]$. In this paper, we investigate…

We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \cite{Ernest1971} and Hughes \cite{Hughes1973} asserts that every weakly compact subset of a locally…

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…