Finite groups all of whose second maximal subgroups are {\mathcal{H }}_p-groups |
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Authors: | Xianggui Zhong Jiakuan Lu Yonggang Li |
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Institution: | 1. Department of Mathematics, Guangxi Normal University, Guilin, 541004, People’s Republic of China
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Abstract: | Let $G$ be a finite group. A subgroup $H$ of $G$ is called an $\mathcal{H }$ -subgroup of $G$ if $N_G(H)\cap H^g\le H$ for all $g\in G$ . A group $G$ is said to be an ${\mathcal{H }}_p$ -group if every cyclic subgroup of $G$ of prime order or order 4 is an $\mathcal{H }$ -subgroup of $G$ . In this paper, the structure of a finite group all of whose second maximal subgroups are ${\mathcal{H }}_p$ -subgroups has been characterized. |
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