Rendiconti del Seminario Matematico della Università di Padova

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Volume 129, 2013, pp. 245–263
DOI: 10.4171/RSMUP/129-14

Published online: 2013-05-15

$SE$-Supplemented Subgroups of Finite Groups

Wenbin Guo[1], Alexander N. Skiba[2] and Nanying Yang[3]

(1) University of Scinece and Technology of China, Hefei, China
(2) Gomel Francisk Skorina State University, Belarus
(3) University of Science and Technology of China, Hefei, China

Let $G$ be a finite group, $H$ a subgroup of $G$ and $H_{seG}$ be the subgroup generated by all subgroups of $H$ which are $S$-quasinormally embedded in $G$. Then we say that $H$ is $SE$-supplemented in $G$ if $G$ has a subgroup $T$ such that $HT=G$ and $H\cap T\leq H_{seG}$. We investigate the influence of $SE$-quasinormally embedded of some subgroups on the structure of finite groups. Our results improve and extend a series of recent results.

Keywords: $S$-quasinormal subgroup, $S$-quasinormally embedded subgroup, $FE$-supplemented subgroup, formation

Guo Wenbin, Skiba Alexander, Yang Nanying: $SE$-Supplemented Subgroups of Finite Groups. Rend. Sem. Mat. Univ. Padova 129 (2013), 245-263. doi: 10.4171/RSMUP/129-14