On weakly s-semipermutable subgroups and the p-nilpotency of finite groups

Abstract

A subgroup H of a group G is called weakly s-semipermutable in G if G has a subnormal subgroup T and an s-semipermutable subgroup H_ssG contained in H such that G = HT and $H\cap T\le H_{\mathit{ssG}}$. In this paper, we present several new criteria on p-nilpotency of finite groups with a small quantity of weakly s-semipermutable maximal subgroups of Sylow p-subgroups.

Keywords:

• Finite group
• generalized p-Fitting subgroup
• p-nilpotent group
• s-semipermutable subgroup
• weakly s-semipermutable subgroup

2020 Mathematics Subject Classification:

• 20D10
• 20D20

Acknowledgments

The authors express their thanks to the referee for his/her useful suggestions.

Additional information

Funding

Projects supported by NSF of China (12061011), NSF of Guangxi (2020GXNSFDA238014) and SRF of Guangxi University (XGZ130761).