Let G be a finite group and $\chi $ be a character of G. The codegree of $\chi $ is ${{\operatorname{codeg}}} (\chi ) ={|G: \ker \chi |}/{\chi (1)}$ . We write $\pi (G)$ for the set of prime divisors of $|G|$ , $\pi ({{\operatorname{codeg}}} (\chi ))$ for the set of prime divisors of ${{\operatorname{codeg}}} (\chi )$ and $\sigma ({{\operatorname{codeg}}} (G))= \max \{|\pi ({{\operatorname{codeg}}} (\chi ))| : \chi \in {\textrm {Irr}}(G)\}$ . We show that $|\pi (G)| \leq ({23}/{3}) \sigma ({{\operatorname{codeg}}} (G))$ . This improves the main result of Yang and Qian [‘The analog of Huppert’s conjecture on character codegrees’, J. Algebra478 (2017), 215–219].

中文翻译：

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于佩尔猜想的类比

让G是一个有限群并且$\吃$成为一个角色G. 共度$\吃$是${{\operatorname{codeg}}} (\chi ) ={|G: \ker \chi |}/{\chi (1)}$. 我们写$\pi (G)$对于素数除数的集合$|G|$,$\pi ({{\operatorname{codeg}}} (\chi ))$对于素数除数的集合${{\operatorname{codeg}}} (\chi )$和$\sigma ({{\operatorname{codeg}}} (G))= \max \{|\pi ({{\operatorname{codeg}}} (\chi ))| : \chi \in {\textrm {Irr}}(G)\}$. 我们表明$|\pi (G)| \leq ({23}/{3}) \sigma ({{\operatorname{codeg}}} (G))$. 这改进了杨和钱的主要结果['于佩尔猜想的类似物关于字符共度'，J.代数478(2017), 215–219]。