On c*-Normal Subgroups of p-Power Order in a Finite Group

Abstract

A subgroup H of a finite group G is called c*-normal in G if there exists a normal subgroup K of G such that G = HK and H ∩ K is S-quasinormally embedded in G. In this paper, the structure of a finite group G with some c*-normal subgroups of Sylow p-subgroups with an any fixed order is characterized and some known related results on p-nilpotency of finite groups are generalized.

Key Words:

• c*-Normal
• p-Nilpotent
• S-Quasinormally embedded
• Finite group
• Saturated formation

2010 Mathematics Subject Classification:

• 20D10

ACKNOWLEDGMENTS

The authors would like to thank the referee for his or her helpful suggestions and comments.

The authors are supported by NSF of China (10961007, 11161006), NSF of Guangxi (0991101, 0991102), and Guangxi Education Department.

Notes

Communicated by V. A. Artamonov.