On an IC-property of subgroups of a finite group

Abstract

Let G be a finite group and H a subgroup of G. We say that H has an IC-property if the intersection of H and $[H,G]$ satisfy some conditions. In this paper, we investigate the structure of a finite group G under the assumption that some maximal subgroups, 2-maximal subgroups, 3-maximal subgroups of G have the IC_p-property and obtain some new characterizations of p-solvable and solvable groups.

Keywords:

• Finite group
• maximal subgroup
• IC-property
• p-solvable

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D20

Acknowledgments

The authors are grateful to the referees and the editors for their valuable comments and specific corrections.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant N. 12301019, 12201495, 12261022, 12301027)