@article {
author = {Alijani, Aliakbar and Sahleh, Hossein},
title = {On T-Extensions of Abelian Groups},
journal = {Khayyam Journal of Mathematics},
volume = {5},
number = {1},
pages = {60-68},
year = {2019},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2018.74220},
abstract = {Let $\Re$ be the category of all discrete abelian groups, and let $\cal{L}$ be the category of all locally compact abelian (LCA) groups. For a group $G\in \cal{L}$, the maximal torsion subgroup of $G$ is denoted by $tG$. A short exact sequence $0\to A\stackrel{\phi}{\to} B\stackrel{\psi}{\to}C\to 0$ in $\Re$ is said to be a t-extension if $0\to tA\stackrel{\phi}{\to} tB\stackrel{\psi}{\to}tC\to 0$ is a short exact sequence. We show that the set of all t-extensions of $A$ by $C$ is a subgroup of $Ext(C,A)$, which contains $Pext(C,A)$ for discrete abelian groups $A$ and $C$. We establish conditions under which the t-extensions split and determine those groups in $\Re$ which are t-injective or t-projective in $\Re$. Finally we determine the compact groups $G$ in $\cal{L}$ such that every pure extension of $G$ by a compact connected group $C\in \cal{L}$ splits.},
keywords = {T-extensions,extensions,pure extensions,locally compact abelian groups},
url = {http://www.kjm-math.org/article_74220.html},
eprint = {http://www.kjm-math.org/article_74220_a9f5d5879c28658ed606d177fed55aa0.pdf}
}