A Generalization of Cover-Avoiding Properties in Finite Groups

Abstract

A subgroup H of a group G is called a CAP*-subgroup of G, if H either covers or avoids every non-Frattini chief factor of G. In this article, we give some interesting properties of CAP*-subgroups. Furthermore, we determine the structure of finite groups based on the assumption that some subgroups are CAP*-subgroups and generalize some known results.

Key Words:

• CAP*-subgroups
• Cover-avoiding properties
• Non-Frattini chief factors
• Saturated formations

2000 Mathematics Subject Classification:

• 20D10
• 20D20

ACKNOWLEDGMENT

The authors would like to thank the referee for his or her valuable suggestions and useful comments contributed to the final version of this article.

Notes

Communicated by P. Tiep.

Supported by the Natural Science Foundation of China and the Natural Science Foundation of Guangxi autonomous region (No. 0249001).