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Even Character Degrees and Ito–Michler Theorem

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Abstract

Let \(\textrm{Irr}_2(G)\) be the set of linear and even-degree irreducible characters of a finite group G. In this paper, we prove that G has a normal Sylow 2-subgroup if \(\sum \limits _{\chi \in \textrm{Irr}_2(G)} \chi (1)^m/\sum \limits _{\chi \in \textrm{Irr}_2(G)} \chi (1)^{m-1} < (1+2^{m-1})/(1+2^{m-2})\) for a positive integer m, which is the generalization of several recent results concerning the well-known Ito–Michler theorem.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huaiyin Normal University, Huaian, 223300, Jiangsu, People’s Republic of China

    Shuqin Dong & Hongfei Pan

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  1. Shuqin Dong
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  2. Hongfei Pan
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Correspondence to Hongfei Pan.

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All authors disclosed no relevant relationships.

Additional information

The first author was supported by NSF of China (Nos. 12201236, 12271200), and the second author by NSF of China (No. 12061011).

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Dong, S., Pan, H. Even Character Degrees and Ito–Michler Theorem. Commun. Math. Stat. (2024). https://doi.org/10.1007/s40304-023-00368-0

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  • DOI: https://doi.org/10.1007/s40304-023-00368-0

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