简单稀土族2𝐹4(𝑞2)的特征码度表征

Pub Date : 2023-05-23 DOI:10.1515/jgth-2022-0119

Yong Yang

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引用次数: 0

摘要

有限群𝐺的一个字符的共轭度为:cod (χ):= | G: ker (χ) | χ¹。\operatorname{cod} (\chi):= \frac{\lvert G:\ker(\chi)\rvert}{\chi(1)}。我们证明了Ree群的余度集合f2²²(q2) {}^{2F＿4}(q{²})(q2 =2²²+1 q²{=2^}2n+1, {n≥1 n}{}\geq 1)决定了群的同构程度。

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A characterization of the simple Ree groups 2𝐹4(𝑞2) by their character codegrees

Abstract The codegree of a character 𝜒 of a finite group 𝐺 is cod ⁡ ( χ ) := | G : ker ⁡ ( χ ) | χ ⁢ ( 1 ) . \operatorname{cod}(\chi):=\frac{\lvert G:\ker(\chi)\rvert}{\chi(1)}. We show that the set of codegrees of the Ree groups F 4 2 ⁢ ( q 2 ) {}^{2}F_{4}(q^{2}) ( q 2 = 2 2 ⁢ n + 1 q^{2}=2^{2n+1} , n ≥ 1 n\geq 1 ) determines the groups up to isomorphism.

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