Weakly s-semipermutable subgroups and the -hypercenter of finite groups

Abstract

In this paper, we investigate the influence of weakly s-semipermutable subgroups on the $p\mathfrak{F}$-hypercenter of a finite group and obtained some new criteria for a normal subgroup to be contained in the $p\mathfrak{F}$-hypercenter of a finite group. Many known results are generalized and uniformed.

Keywords:

• Formation
• p$\mathfrak{F}$-hypercenter
• supersolvable
• weakly s-semipermutable

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D20

Acknowledgments

The authors are grateful to the referees and the editors for their valuable comments and specific corrections.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871360, 11901417).