S-semiembedded subgroups of finite groups

Abstract

A subgroup H of a finite group G is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. We say that a subgroup H of a finite group G is S-semiembedded in G if there exists an s-permutable subgroup T of G such that TH is s-permutable in G and T\cap H\le H_{\overline{s}G}, where H_{\overline{s}G} is an s-semipermutable subgroup of G contained in H. In this paper, we investigate the influence of S-semiembedded subgroups on the structure of finite groups.

Key words： s-Permutable subgroup; s-semipermutable subgroup; supersoluble group; S-semiembedded subgroup; p-nilpotent group

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