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On f-Hypercentral Actions of Finite Group

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Abstract

Let f be a formation function and G an A-group. It is said that A acts f-hypercentrally on G if A acts f-centrally on every A-composition factor of G. In this paper, groups are investigated by f-hypercentral actions. In particular, some well-known results, including a theorem of Huppert and a theorem of Hall–Higman, are generalized.

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Acknowledgements

The authors are grateful to the referees for their helpful reports.

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Authors and Affiliations

  1. School of Sciences, Nantong University, Nantong, 226019, Jiangsu, People’s Republic of China

    Baojun Li & Lü Gong

Authors
  1. Baojun Li
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  2. Lü Gong
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Correspondence to Baojun Li.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 11471055)

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Li, B., Gong, L. On f-Hypercentral Actions of Finite Group. Commun. Math. Stat. 9, 521–533 (2021). https://doi.org/10.1007/s40304-020-00232-5

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  • DOI: https://doi.org/10.1007/s40304-020-00232-5

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