2018
Том 70
№ 1

# On ss-quasinormal and weakly s-supplemented subgroups of finite groups

Abstract

Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is called $ss$-quasinormal in $G$ if there is a subgroup $B$ of $G$ such that $G = HB$ and $H$ permutes with every Sylow subgroup of $B$; $H$ is called weakly $s$-supplemented in G if there is a subgroup T of G such that $G = HT$ and $H \bigcap T \leq H_{sG}$, where $H_{sG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are $s$-quasinormal in $G$. In this paper we investigate the influence of $ss$-quasinormal and weakly $s$-supplemented subgroups on the structure of finite groups. Some recent results are generalized and unified.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 12, pp 1641-1659.

Citation Example: Li C., Li Yangming On ss-quasinormal and weakly s-supplemented subgroups of finite groups // Ukr. Mat. Zh. - 2011. - 63, № 12. - pp. 1623-1631.

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