TY - JOUR
ID - 74220
TI - On T-Extensions of Abelian Groups
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Alijani, Aliakbar
AU - Sahleh, Hossein
AD - Mollasadra Technical and Vocational College, Technical and Vocational University, Ramsar, Iran.
AD - Department of Mathematics, University of Guilan, P. O. Box 1914, Rasht, Iran.
Y1 - 2019
PY - 2019
VL - 5
IS - 1
SP - 60
EP - 68
KW - T-extensions
KW - extensions
KW - pure extensions
KW - locally compact abelian groups
DO - 10.22034/kjm.2018.74220
N2 - 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.
UR - http://www.kjm-math.org/article_74220.html
L1 - http://www.kjm-math.org/article_74220_a9f5d5879c28658ed606d177fed55aa0.pdf
ER -