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Finite Groups with Some Bounded Codegrees

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Abstract

For a character χ of a finite group G, the number cod(χ)≔ ∣G: ker(χ)∣/χ(1) is called the codegree of χ. In this paper, we give a solvability criterion for a finite group G depending on the minimum of the ratio χ(1)2/cod(χ), when χ varies among the irreducible characters of G.

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Acknowledgements

We would like to thank reviewers for their comments, which are all valuable and very helpful for revising and improving our paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. China

    Dong Fang Yang & Heng Lv

  2. Department of Mathematics, Changshu Institute of Technology, Changshu, 215500, P. R. China

    Yu Zeng

Authors
  1. Dong Fang Yang
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  2. Yu Zeng
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  3. Heng Lv
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Correspondence to Heng Lv.

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Conflict of Interest The authors declare no conflict of interest.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11971391, 12071376, 12301018, 12171058, 12326356), the Natural Science Foundation of Jiangsu Province (Grant No. BK20231356) and the Natural Science Foundation for the Universities in Jiangsu Province (Grant No. 23KJB110002). The first and second authors are supported by the Chinese Scholarship Council

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Yang, D.F., Zeng, Y. & Lv, H. Finite Groups with Some Bounded Codegrees. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-1236-0

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  • DOI: https://doi.org/10.1007/s10114-024-1236-0

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