On second maximal subgroups with core relation in finite groups

Abstract

In this paper, we will investigate the structure of groups with the property of the core relation between some second maximal subgroups and corresponding maximal subgroups, and obtained some new results about finite groups.

ARTICLE HISTORY Received 7 September 2023 Revised 13 December 2023 Communicated by Mandi Schaeffer Fry

KEYWORDS:

• $\Phi$-simple subgroups
• Frattini subgroups
• maximal subgroups
• second maximal subgroups
• the core of subgroups

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D20

Additional information

Funding

This research is supported by NSFC (Grant # 12371018, 11871062), Fundamental Research Funds for the Central Universities (Grant # 1014/418240, 1014/423135), NSFC-RFBR (Grant # 12011530061) and Tianshan Youth Talent Project of Xinjiang Uygur Autonomous Region (Grant # 2020Q023).