Keyword: Hall S-semiembedded Subgroup : Search

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$𝔉$ $𝔉$ -groups and Hall $s$ $s$ -semiembedded subgroups
- Yanhui Guo and
- Xianhua Li
Journal of Algebra and Its Applications01 Mar 2017
Preview Abstract
Let $G$ $G$ be a finite group. A subgroup $H$ $H$ of $G$ $G$ is said to be a Hall $s$ $s$ -semiembedded subgroup of $G$ $G$ if $H$ $H$ is a Hall subgroup of $〈 H, P 〉$ $〈 H, P 〉$ for any $P \in {Syl}_{p} (G)$ $P \in {Syl}_{p} (G)$ , where $(p, | H |) = 1$ $(p, | H |) = 1$ . In this paper, we investigate the influence of Hall $s$ $s$ -semiembedded subgroups on the structure of the finite group $G$ $G$ . Some new results about $G$ $G$ to be a $𝔉$ $𝔉$ -group are obtained, where $𝔉$ $𝔉$ is a saturated formation.

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