Finite Groups with Some Subgroups of Prime Power Order S-Quasinormally Embedded

Abstract

A subgroup of a group G is said to be S-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be S-quasinormally embedded in G if every Sylow subgroup of H is a Sylow subgroup of some S-quasinormal subgroup of G. In this paper we examine the structure of a finite group G under the assumption that certain abelian subgroups of prime power order are S-quasinormally embedded in G. Our results improve and extend recent results of Ramadan [Ramadan, M. (2001). The influence of S-quasinormality of some subgroups of prime power order on the structure of finite groups. Arch. Math. 77:143–148].

Key Words:

• S-Quasinormally embedded subgroup
• Generalized hypercenter subgroup
• Generalized supersolvably embedded subgroup
• Supersolvable group

MSC:

• 20D10
• 20D20

Notes

^#Communicated by A. Turull.