On the Solvability of a Finite Group with S-Seminormal Schmidt Subgroups

Abstract

A finite nonnilpotent group is called a Schmidt group if all its proper subgroups are nilpotent. A subgroup A is called S-seminormal (or SS-permutable) in a finite group G if there is a subgroup B such that G = AB and A is permutable with every Sylow subgroup of B. We establish criteria for the solvability and 𝜋-solvability of finite groups in which some Schmidt subgroups are S-seminormal. In particular, we prove the solvability of a finite group in which all supersoluble Schmidt subgroups of even order are S-seminormal.