Rendiconti del Seminario Matematico della Università di Padova


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

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

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

(1) School of Mathematical Sciences, Xuzhou Normal University, 221116, Xuzhou, China
(2) School of Mathematical Sciences, University of Scinece and Technology of China, 230026, Hefei, Anhui, China
(3) School of Mathematical Sciences, Huaiyin Normal University, 223300, Huaiyin, 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