Finite nonprimarily factorizable groups
Let H be an extension of an elementary abelian p-group by a group of prime order q, \(p\neq q\); then H is called quasielementary group. Theorem. The following assertions are equivalent: (a) Every quasielementary subgroup of G is complemented. (b) Every non-primary subgroup of G is complemented. \textit{Eh. S. Alekseeva} [in Groups with systems of complemented subgroups, 147-179 (1971; Zbl 0276.20019)] has classified all finite groups with property (b).
scientific article; zbMATH DE number 3979350