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AN ANALOGUE OF HUPPERT’S CONJECTURE FOR CHARACTER CODEGREES
Bulletin of the Australian Mathematical Society ( IF 0.7 ) Pub Date : 2021-02-08 , DOI: 10.1017/s0004972721000046
A. BAHRI , Z. AKHLAGHI , B. KHOSRAVI

Let G be a finite group, let ${\mathrm{Irr}}(G)$ be the set of all irreducible complex characters of G and let $\chi \in {\mathrm{Irr}}(G)$ . Define the codegrees, ${\mathrm{cod}}(\chi ) = |G: {\mathrm{ker}}\chi |/\chi (1)$ and ${\mathrm{cod}}(G) = \{{\mathrm{cod}}(\chi ) \mid \chi \in {\mathrm{Irr}}(G)\} $ . We show that the simple group ${\mathrm{PSL}}(2,q)$ , for a prime power $q>3$ , is uniquely determined by the set of its codegrees.

中文翻译:

HUPPERT 猜想的字符编码类比

G是一个有限群,令${\mathrm{Irr}}(G)$是所有不可约复特征的集合G然后让$\chi \in {\mathrm{Irr}}(G)$. 定义共度,${\mathrm{cod}}(\chi ) = |G: {\mathrm{ker}}\chi |/\chi (1)$${\mathrm{cod}}(G) = \{{\mathrm{cod}}(\chi ) \mid \chi \in {\mathrm{Irr}}(G)\} $. 我们证明了简单群${\mathrm{PSL}}(2,q)$, 为素幂$q>3$, 由其共度的集合唯一确定。
更新日期:2021-02-08
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