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.
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).