On s-Semipermutable Maximal and Minimal Subgroups of Sylow p-Subgroups of Finite Groups

ABSTRACT

A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|,|K|) = 1. H is said to be s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p,|H|) = 1. In this article, we investigate the p-nilpotency of a group for which every maximal subgroup of its Sylow p-subgroups is s-semipermutable for some prime p. We generalize some recent theorems in Guo and Shum (2003).

Communicated by M. Dixon.

Keywords:

• p-nilpotent group
• Saturated formation
• Semipermutable

2000 Mathematics Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENT

Project supported in part by NSF of China, NSF of Guangdong, Fund from Education Ministry of China and ARC of ZSU.