On the solvability of a finite group with S-seminormal Schmidt subgroups - Zubei, E. V.; Knyagina, V. N.; Monakhov, V. S. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
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 the criteria of 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.