TY - JOUR
ID - 4435
TI - Splitting of extensions in the category of locally compact abelian groups
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Sahleh, Hossein
AU - Alijani, Akbar
AD - Department of Mathematics
University of Guilan
AD - University of Guilan
Y1 - 2014
PY - 2014
VL - 3
IS - 3
SP - 39
EP - 45
KW - Locally compact abelian group
KW - Splitting of Extension
KW - Divisible group
DO - 10.22108/ijgt.2014.4435
N2 - Let $\pounds$ be the category of all locally compact abelian (LCA) groups. In this paper, the groups $G$ in $\pounds$ are determined such that every extension $0\to X\to Y\to G\to 0$ with divisible, $\sigma-$compact $X$ in $\pounds$ splits. We also determine the discrete or compactly generated LCA groups $H$ such that every pure extension $0\to H\to Y\to X\to 0$ splits for each divisible group $X$ in $\pounds$.
UR - https://ijgt.ui.ac.ir/article_4435.html
L1 - https://ijgt.ui.ac.ir/article_4435_22e1c3d0e09071cafadb580f175adec2.pdf
ER -