Related papers: On TFU extensions in LCA groups

Let G and C be two discrete abelian groups. It is known that Pext(C,G) is a subgroup of Ext(C,G). In this paper, we introduce the t-extensions of G by C. We will show that the set of all t-extensions of G by C is a subgroup of Ext(C,G)…

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…

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…

Let $A$ be a unital separable amenable \CA and $C$ be a unital \CA with certain infinite property. We show that two full monomorphisms $h_1, h_2: A\to C$ are approximately unitarily equivalent if and only if $[h_1]=[h_2]$ in $KL(A,C).$ Let…

Let $A$ be a unital separable \CA and $B=C\otimes {\cal K},$ where $C$ is a unital \CA. Let $\tau: A\to M(B)/B$ be a weakly unital full essential extensions of $A$ by $B.$ We show that there is a bijection between a quotient group of…

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 $X$ 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…

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…

We extend to the context of algebraic groups a classic result on extensions of abstract groups relating the set of isomorphism classes of extensions of $G$ by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof should be…

A twisted sum in the category of topological abelian groups is a short exact sequence $0\to Y\to X \to Z\to 0$ where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is equivalent to $0\to Y\to…

Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence…

We say that a subgroup $H$ of an infinite compact Abelian group $X$ is {\it $T$-characterized} if there is a $T$-sequence $\mathbf{u} =\{u_n \}$ in the dual group of $X$ such that $H=\{x\in X: \; (u_n, x)\to 1 \}$. We show that a closed…

We sudy the behaviour of endomorphisms and automorphisms of groups involved in abelian group extensions. The main result can be stated as follows: Let $0\to N\to G\to Q \to 1$ be an abelian group extension. Then one has the following exact…

When a pair of \'etale groupoids $\mathcal{G}$ and $\mathcal{G}'$ on totally disconnected spaces are related in some way, we discuss the difference of their homology groups. More specifically, we treat two basic situations. In the…

In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in…

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…

We compute the {\Omega}^1(G) invariant when 1 {\to} H {\to} G {\to} K {\to} 1 is a split short exact sequence. We use this result to compute the invariant for pure and full braid groups on compact surfaces. Applications to twisted conjugacy…

A Hausdorff topological group G is minimal if every continuous isomorphism f : G --> H between G and a Hausdorff topological group H is open. Clearly, every compact Hausdorff group is minimal. It is well known that every infinite compact…

Let $A$ and $B$ be separable $C^*$-algebras, $A$ unital and $B$ stable. It is shown that there is a natural six-terms exact sequence which relates the group which arises by considering all semi-split extensions of $A$ by $B$ to the group…

This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and…