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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 1, Pages 310–318
(Mi timm1283)
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This article is cited in 1 scientific paper (total in 1 paper)
On $S\Phi$-embedded subgroups of finite groups
L. Zhanga, Guo Wen Bina, L. Huob a University of Science and Technology of China, Anhui, Hefei
b Chongqing University of Technology
Abstract:
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, $p$-supersolvable group, $p$-nilpotent group.
Received: 10.12.2015
Citation:
L. Zhang, Guo Wen Bin, L. Huo, “On $S\Phi$-embedded subgroups of finite groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 310–318
Linking options:
https://www.mathnet.ru/eng/timm1283 https://www.mathnet.ru/eng/timm/v22/i1/p310
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Abstract page: | 497 | Full-text PDF : | 97 | References: | 72 | First page: | 38 |
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