Rendiconti del Seminario Matematico della Università di Padova


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Volume 139, 2018, pp. 129–142
DOI: 10.4171/RSMUP/139-3

Published online: 2018-06-06

On $W$-$S$-permutable subgroups of finite groups

Jinxin Gao[1] and Xiuyun Guo[2]

(1) Shanghai University, China
(2) Shanghai University, China

A subgroup $H$ of a finite group $G$ is said to be $W$-$S$-permutable in $G$ if there is a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K$ is a nearly $S$-permutable subgroup of $G$. In this article, we analyse the structure of a finite group $G$ by using the properties of $W$-$S$-permutable subgroups and obtain some new characterizations of finite $p$-nilpotent groups and finite supersolvable groups. Some known results are generalized

Keywords: $W-S$-permutable subgroup; $p$-nilpotent group; maximal subgroup; minimal subgroup; saturated formation

Gao Jinxin, Guo Xiuyun: On $W$-$S$-permutable subgroups of finite groups. Rend. Sem. Mat. Univ. Padova 139 (2018), 129-142. doi: 10.4171/RSMUP/139-3