Rendiconti del Seminario Matematico della Università di Padova


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Volume 133, 2015, pp. 79–90
DOI: 10.4171/RSMUP/133-3

Published online: 2015-06-01

Finite $p$-supersoluble groups with some $E$-$S$-supplemented subgroups

Changwen Li[1], Xiaolong Yu[2] and Na Tang[3]

(1) Xuzhou Normal University, China
(2) University of Scinece and Technology of China, Hefei, Anhui, China
(3) Huaiyin Normal University, China

Let $H$ be a subgroup of a group $G$ and $H_{eG}$ denote the subgroup of $H$ generated by all those subgroups of $H$ which are $S$-permutably embedded in $G$. $H$ is said to be $E$-$S$-supplemented in $G$ if there exists a subnormal subgroup $T$ of $G$ such that $G=HT$ and $H\cap T\leq H_{eG}$. In this paper, we investigate the influence of some $E$-$S$-supplemented subgroups on the structure of finite group. Some new characterizations of $p$-supersoluble groups are obtained.

Keywords: $S$-permutable, $E-S$-supplemented, $p$-supersoluble

Li Changwen, Yu Xiaolong, Tang Na: Finite $p$-supersoluble groups with some $E$-$S$-supplemented subgroups. Rend. Sem. Mat. Univ. Padova 133 (2015), 79-90. doi: 10.4171/RSMUP/133-3