A note on a theorem of Megibben

Peter Vassilev Danchev; Patrick Keef

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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 $G \in 𝕂$ , a class of abelian groups, does imply that $A \in 𝕂$ . 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 $𝕂$ coincides with the class of all totally projective $p$ -groups. ...