论文标题
不可约字符的共同学位的组是不同的
Groups in which the co-degrees of the irreducible characters are distinct
论文作者
论文摘要
令$ g $为有限的组，让$ \ rm {irr}（g）$为$ g $的所有不可减少复杂字符的集合。对于一个字符$χ\ in \ rm {irr}（g）$，数字$ \ rm {cod}（χ）（χ）：= | g：\ rm {ker}χ|/χ（1）$称为$χ$的共二级。 $ g $的所有不可约字符的共同点集用$ \ rm {cod}（g）$表示。在本文中，我们表明，对于非平凡的有限组$ g $，$ | \ rm {irr}（g）| = | \ rm {cod}（cod}（g）| $ i时，并且仅当$ g $与cyclic Group $ \ mathbb {Z} _2 $ _2 $或对称的组$ s $ s_s_3 $ s_3 $ s_3 $ s_3 $ s_3 $ s_3 $。
Let $G$ be a finite group and let $\rm{Irr}(G)$ be the set of all irreducible complex characters of $G$. For a character $χ\in \rm{Irr}(G)$, the number $\rm{cod}(χ):=|G:\rm{ker}χ|/χ(1)$ is called the co-degree of $χ$. The set of co-degrees of all irreducible characters of $G$ is denoted by $\rm{cod}(G)$. In this paper, we show that for a non-trivial finite group $G$, $|\rm{Irr}(G)|=|\rm{cod}(G)|$ if and only if $G$ is isomorphic to the cyclic group $\mathbb{Z}_2$ or the symmetric group $S_3$.
