Abstract
Let G be a p-solvable finite group for some prime p, \(G_{p'}\) a \(p'\)-Hall subgroup of G and x a p-regular element of G. Clearly, \(\langle x\rangle \le C_G(x)\le G\). Notice that the structure of \(G_{p'}\) is easily decided when \(C_G(x)=\langle x\rangle \) and \(C_G(x)=G\) for every p-regular element x of G. So, in this paper, we investigate the structure of \(G_{p'}\) by assuming that \(C_G(x)\) is maximal in G for every non-central p-regular element x of G.
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The authors would like to thank the referee for their valuable suggestions and useful comments contributed to the final version of this paper.
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The research of the work was supported by the National Natural Science Foundation of China (11501176, 11901169), the project for high quality courses of postgraduate education in Henan Province, Research and practice project of higher education reform in Henan Normal University (post-graduate education, No. YJS2019JG06) and Key Laboratory of Applied Mathematics of Fujian Province University (Putian University, No. SX201902).
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Zhao, X., Chen, R., Zhou, Y. et al. On the centralizers of the p-regular elements in a finite group. Bull Braz Math Soc, New Series 52, 353–360 (2021). https://doi.org/10.1007/s00574-020-00207-8
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DOI: https://doi.org/10.1007/s00574-020-00207-8