2019
Том 71
№ 11

All Issues

Zubei E. V.

Articles: 1
Article (Russian)

On the solvability of a finite group with $S$-seminormal Schmidt subgroups

Knyagina V. N., Monakhov V. S., Zubei E. V.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 11. - pp. 1511-1518

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 $\pi$ -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.