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Nonsolvable groups whose irreducible character degrees have special 2-parts

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Abstract

Let G be a nonsolvable group and Irr(G) the set of irreducible complex characters of G. We consider the nonsolvable groups whose character degrees have special 2-parts and prove that if χ(1)2 = 1 or ∣G∣2 for every χ ∈ Irr(G), then there exists a minimal normal subgroup N of G such that N ≅ PSL(2, 2n) and G/N is an odd order group.

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Acknowledgements

The author is indebted to the referees for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871011, 11701421) and the Science & Technology Development Fund of Tianjin Education Commission for Higher Education (2020KJ010).

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  1. School of Mathematical Science, Tianjin Normal University, Tianjin, 300387, China

    Yang Liu

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  1. Yang Liu
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Correspondence to Yang Liu.

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Liu, Y. Nonsolvable groups whose irreducible character degrees have special 2-parts. Front. Math 17, 1083–1088 (2022). https://doi.org/10.1007/s11464-021-0984-8

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  • DOI: https://doi.org/10.1007/s11464-021-0984-8

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