A result on s-semipermutable subgroups of finite groups and some applications

Abstract

Abstract–Let p be a prime number, G be a p-solvable finite group and P be a Sylow p-subgroup of G. We prove that G is p-supersolvable if $N_G(P)$ is p-supersolvable and if there is a subgroup H of P with $P\prime \le H\le \Phi (P)$ such that H is s-semipermutable in G. As applications, we simplify the proofs of some known results and also generalize some known results.

Keywords:

• Finite groups
• p-supersolvable
• p-nilpotent
• s-semipermutable
• s-permutable
• pronormal
• weakly $\mathit{H}$-subgroup
• c-supplemented

2020MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D20

Disclosure Statement

The authors report there are no competing interests to declare.