# 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 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.
Published

25.11.2018

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 70, no. 11, Nov. 2018, pp. 1511-8, http://umj.imath.kiev.ua/index.php/umj/article/view/1654.

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Section

Research articles