c^∗-Quasinormally embedded subgroups of finite groups

Abstract

Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing |H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called c^∗-quasinormally embedded in G if there is a subgroup T of G such that G = HT and H∩T is s-quasinormally embedded in G.We investigate the influence of c^∗-quasinormally embedded subgroups on the structure of finite groups. Some recent results are generalized.

Key words： c^∗-Quasinormally embedded subgroup; p-nilpotent; supersolvable; Sylow subgroup

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