Rendiconti del Seminario Matematico della Università di Padova


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

$SE$-Supplemented Subgroups of Finite Groups

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

(1) School of Mathematical Sciences, University of Scinece and Technology of China, 230026, Hefei, Anhui, China
(2) Department of Mathematics, Gomel Francisk Skorina State University, 246019, Gomel, Belarus
(3) School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, Anhui, 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