On weakly s_p-permutable subgroups of finite groups

Abstract

Let G be a finite group, H a subgroup of G and p a prime number. We say that H is weakly s_p-permutable in G if G has a subnormal subgroup K such that G = HK, $H_{sG}\le K$ and $|H\cap K:H_{sG}|$ is a $p^{\prime }$-number, where H_sG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. In this paper, we investigate the structure of a group G under the assumption that certain subgroups of G are weakly s_p-permutable in G. Some recent results are extended and generalized.

Communicated by Alexander Olshanskii

KEYWORDS:

• c-normal subgroup
• cp-normal subgroup
• s-permutable subgroup
• weakly s-permutable subgroup

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D15
• 20D20

Acknowledgment

The authors are very grateful for the helpful suggestions of the referee.