Second Maximal Subgroups of a Sylow p-Subgroup and the p-Nilpotency of Finite Groups

Abstract

A subgroup H of a group G is said to be weakly s-semipermutable in G if G has a subnormal subgroup T such that HT = G and H ∩ T ≤ ${H}_{\overline{s}G}$ , where ${H}_{\overline{s}G}$ is the subgroup of H generated by all subgroups of H that are s-semipermutable in G. The main aim of the paper is to study the p-nilpotency of a group for which every second maximal subgroup of its Sylow p-subgroups is weakly s-semipermutable. Some new results are obtained.