On s-semipermutable maximal and minimal subgroups of Sylow p-subgroups of finite groups

A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with (vertical bar H vertical bar, vertical bar K vertical bar) = 1. H is said to be s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p, vertical bar H vertical bar) = 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).