On complementability of nonmetacyclic subgroups in finite \(A\)-groups (Q2784886)

The author continues studying finite solvable groups with Abelian Sylow subgroups. In a sequence of preceding papers he investigated such groups with complemented non-metacyclic subgroups under various conditions on the group. In this paper such groups \(G\) with elementary Abelian Sylow subgroups and non-primary metacyclic second derived subgroup \(G''\) are considered. The main theorem gives a certain description of such groups via their representation as semidirect products of some groups which are near to groups with complemented subgroups.