On weakly S-embedded subgroups and weakly τ-embedded subgroups

الأصل · EN

Let G be a finite group. A subgroup H of G is said to be weakly S-embedded in G if there exists K G such that HK is S-quasinormal in G and H∩ K≤ HseG, where HseG is the subgroup generated by all those subgroups of H which are S-quasinormally embedded in G. We say that H is weakly τ-embedded in G if there exists K G such that HK is S-quasinormal in G and H∩ K≤ HτG, where HτG is the subgroup generated by all those subgroups of H which are τ-quasinormal in G. In this paper, we study the properties of the weakly S-embedded subgroups and the weakly τ-embedded subgroups, and use them to determine the structure of finite groups.