Geodesic
On $S\Phi$-embedded subgroups of finite groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 310-318

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A subgroup $H$ of $G$ is called $S\Phi$-embedded in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is $S$-quasinormal in $G$ and $(H \cap T)H_{G}/H_{G}\leq\Phi(H/H_{G})$, where $H_{G}$ is the maximal normal subgroup of $G$ contained in $H$ and $\Phi(H/H_{G})$ is the Frattini subgroup of $H/H_{G}$. In this paper, we investigate the influence of $S\Phi$-embedded subgroups on the structure of finite groups. In particular, some new characterizations of $p$-supersolvability of finite groups are obtained by assuming some subgroups are $S\Phi$-embedded.
Keywords: sylow $p$-subgroup, $S\Phi$-embedded subgroup, $p$-nilpotent group.
Mots-clés : $p$-supersolvable group 
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L. Zhang; Guo Wen Bin; L. Huo. On $S\Phi$-embedded subgroups of finite groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 310-318. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a29/