On finite groups in which every maximal subgroup of order divisible by $p$ is $p$-decomposable

Year 2025, Volume: 54 Issue: 5, 1725 - 1729, 29.10.2025

Qianqian Wang , Shijie Tao

https://doi.org/10.15672/hujms.1577338

Abstract

We obtain a complete classification of a finite group $G$ in which every maximal subgroup of order divisible by $p$ is $p$-decomposable for a given prime divisor $p$ of |$G$| and our results generalize a recent result of Shi and Tian.

Keywords

maximal subgroup , p-decomposable group , inner p-decomposable , Sylow subgroup

Ethical Statement

This study adheres to the principles of academic integrity, with all research steps and results accurately presented to ensure the rigor of the mathematical models and derivations. The theoretical frameworks and references used in this study are clearly cited to respect intellectual property rights, and all data, models, and theoretical methods utilized comply with citation standards.

Supporting Institution

National Natural Science Foundation of China,e Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications

Project Number

Nos. 12471017, 12071181 Nos. NY 222090, NY 222091

Thanks

The authors are supported by the National Natural Science Foundation of China (Nos. 12471017,12071181) and the Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications (Grant Nos. NY 222090, NY 222091)

References

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