Том 70
№ 4

All Issues

Li C.

Articles: 2
Brief Communications (English)

A note on $SΦ$-supplemented subgroups

Li C., Yi X., Zhang X.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1139-1141

We give new and brief proofs of the results obtained by X. Li and T. Zhao in [\mathrm{S}\Phi -supplemented subgroups of finite groups // Ukr. Math. J. – 2012. – 64, № 1. – P. 102–109].

Article (English)

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

Li C., Li Yangming

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 12. - pp. 1623-1631

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.