Suppose $A$ is an abelian torsion group with a subgroup $G$ such that $A/G$ is countable that is, in other words, $A$ is a torsion countable abelian extension of $G$. A problem of some group-theoretic interest is that of whether $G \in \mathbb K$, a class of abelian groups, does imply that $A\in \mathbb K$. The aim of the present paper is to settle the question for certain kinds of groups, thus extending a classical result due to Wallace (J. Algebra, 1981) proved when $\mathbb K$ coincides with the class of all totally projective $p$-groups.
@article{107957,
author = {Peter Vassilev Danchev},
title = {Countable extensions of torsion Abelian groups},
journal = {Archivum Mathematicum},
volume = {041},
year = {2005},
pages = {265-272},
zbl = {1114.20030},
mrnumber = {2188382},
language = {en},
url = {http://dml.mathdoc.fr/item/107957}
}
Danchev, Peter Vassilev. Countable extensions of torsion Abelian groups. Archivum Mathematicum, Tome 041 (2005) pp. 265-272. http://gdmltest.u-ga.fr/item/107957/
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