On SQ-Supplemented Subgroups of Finite Groups

Abstract

Let G be a finite group and H ≤ G. The subgroup H is called: S-permutable in G if HP = PH for all Sylow subgroups P of G; S-permutably embedded in G if each Sylow subgroup of H is also a Sylow subgroup of some S-permutable subgroup of G. Let H be a subgroup of a group G. Then we say that H is SQ-supplemented in G if G has a subgroup T and an S-permutably embedded subgroup C ≤ H such that HT = G and T ∩ H ≤ C. We study the structure of G under the assumption that some subgroups of G are SQ-supplemented in G. Some known results are generalized.