Abstract
In this note, we obtain a criterion for p-nilpotency of a finite group by analyzing the intersections between \(O^{p}(G)\) and p-sylowizers of some p-subgroups with given order. Our main result not only simplifies, but also generalizes some main theorems of Lei and Li (Arch Math (Basel) 114(4):367–376, 2020), and Li and Zhang (Arch Math (Basel) 116(3):251–259, 2021).
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Acknowledgements
The authors are grateful to the referee who provided his/her valuable suggestions. Haoran Yu is supported by the China Postdoctoral Science Foundation (Grant No. 2018M630317 and 2019T120231), the National Natural Science Foundation of China (Grant No. 12001225 and 11871241), and the Education Department Project of Jilin Province (Grant No. JJKH20211033KJ). Xiaowei Xu is supported by the National Natural Science Foundation of China (Grant No. 11971289).
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Yu, H., Du, M. & Xu, X. A note on p-sylowizers of p-subgroups in finite groups. Arch. Math. 118, 13–17 (2022). https://doi.org/10.1007/s00013-021-01668-z
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DOI: https://doi.org/10.1007/s00013-021-01668-z