FINITE GROUPS WITH SOME SEMI-p-COVER-AVOIDING OR S-QUASINORMALLY EMBEDDED SUBGROUPS

Abstract

A subgroup H of a group G is called S-quasinormally embedded in G if, for each prime p dividing the order of H, a Sylow p-subgroup of H is a Sylow p-subgroup of an S-quasinormal subgroup of G. H is said to be semi-p-cover-avoiding in G if there is a chief series 1 = G0 < G1 < ⋯ < Gt = G of G such that, for every i = 1, 2, ⋯, t, if Gi/Gi-1 is a p-chief factor, then H either covers or avoids Gi/Gi-1. We give the structure of a finite group G in which some subgroups of G with prime-power order are either semi-p-cover-avoiding or S-quasinormally embedded in G.