A note on a result of Aseeri and Kaspczyk about p-supersolvability of finite groups

Abstract

Let G be a p-solvable finite group, where p is a prime dividing the order of G, and P be a Sylow p-subgroup of G. In this short note, we prove that the p-length of G is 1 if there is a subgroup H of P with $P\prime \le H\le \Phi (P)$ such that H is s-semipermutable or s-permutably embedded in G. Our result not only simplifies, but also generalizes some main theorems of Aseeri and Kaspczyk [A result on s-semipermutable subgroups of finite groups and some applications, Commun. Algebra (2023)].

Keywords:

• Formation
• p-supersolvable
• p-nilpotent
• s-permutably embedded subgroups
• s-semipermutable subgroups

2020 Mathematics Subject Classification:

• 20D10

Acknowledgments

The authors are grateful to the referee who provided his/her valuable suggestions.

Additional information

Funding

Haoran Yu is supported by National Natural Science Foundation of China (Grant No. 12001225 and 12171194), and the Science and Technology Department Project of Jilin Province (Grant No. 20210508024RQ).