Nearly s-embedded subgroups and the p-nilpotency of finite groups

Abstract

A subgroup H of a finite group G is said to be nearly s-embedded in G if G has an s-permutable subgroup T and an s-semipermutable subgroup HssG contained in H such that $H^{sG}=HT$ and $H\cap T\le H_{\mathit{ssG}},$ where HsG is the intersection of all s-permutable subgroups of G containing H. In this article, we investigate the influence of some nearly s-embedded subgroups of Sylow p-subgroups on the p-nilpotency of finite groups. A number of known results are improved and extended.

Keywords:

• Nearly s-embedded
• p-nilpotency
• s-permutable
• s-semipermutable

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D15
• 20D20

Additional information

Funding

Projects supported by NSF of China (11361006), SRF of Guangxi University (XGZ130761) and Guangxi University for Nationalities (2016MDYB022).