Invariant TI-subgroups or subnormal subgroups and structure of finite groups

Abstract

Let G and A be finite groups of relative coprime orders and A acts on G via automorphisms. When certain A-invariant subgroups of G are TI-subgroups or subnormal subgroups, we study the solubility and other structure properties of G.

Keywords:

• Coprime action
• invariant subgroup
• soluble group

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D10
• 20D20

Acknowledgments

We thank the anonymous referee for his/her comments, that have helped us to improve the presentation of the paper.

Additional information

Funding

J. Lu is supported by the Guangxi Natural Science Foundation Program (2020GXNSFAA238045); B. Zhang is supported by the Guangxi Basic Ability Promotion Project for Young and Middle-aged Teachers (2020KY02019); W. Meng is supported by then National Natural Science Foundation of China (12161021) and the Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation.