Even Character Degrees and Ito–Michler Theorem

Shuqin Dong , Hongfei Pan

Communications in Mathematics and Statistics ›› : 1 -10.

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Communications in Mathematics and Statistics ›› : 1 -10. DOI: 10.1007/s40304-023-00368-0
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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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Character degrees / Sylow subgroups

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Shuqin Dong, Hongfei Pan. Even Character Degrees and Ito–Michler Theorem. Communications in Mathematics and Statistics 1-10 DOI:10.1007/s40304-023-00368-0

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National Natural Science Foundation of China(12201236)

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