On finite $A$-groups with complementable nonmetacyclic subgroups

Abstract

We study groupsG satisfying the following conditions:
(i)G is a finite solvable group with non-Abelian commutant and Abelian Sylow subgroups;
(ii) all nonmetacyclic subgroups ofG are complementable.
We give a description of the structure of such groups with nonmetacyclic second commutant.