On weakly H-subgroups of finite groups II*

Abstract

Let G be a group. A subgroup H of G is called an $\mathcal{H}$-subgroup in G if $N_G(H)\cap H^x\le H$ for all $x\in G.$ Furthermore, a subgroup H of G is called a weakly $\mathcal{H}$-subgroup in G if there exists a normal subgroup K of G such that G = HK and $H\cap K$ is an $\mathcal{H}$-subgroup in G. In this article, some new criteria for a group to be p-nilpotent and supersolvable are given.

Keywords:

• p-nilpotent group
• supersolvable group
• weakly $\mathcal{H}$-subgroup

2020 Mathematics Subject Classification:

• 20D10
• 20D20

Acknowledgements

The authors are indebted to the referees for valuable suggestions and very careful reading of the original manuscript.

Additional information

Funding

The research of the work is supported by the National Natural Science Foundation of China (11901169) and Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Sciences, Henan Normal University.