论文标题
$ k_4 $ - 直径的免费字符图三
$K_4$-free character graphs with diameter three
论文作者
论文摘要
令$ g $为有限的组，让$ \ rm {irr}（g）$为$ g $的所有不可减少复杂字符的集合。令$ \ rm {cd}（g）$是$ g $的所有字符度的集合，并用$ρ（g）$表示the $ rm {cd}（g）$的素质。与$ g $相关的字符图$δ（g）$是一个图形，其顶点集为$ρ（g）$，并且在两个不同的Primes $ p $和$ q $之间存在优势，并且仅当产品$ pq $划分$ g $的某些字符。假设字符图$δ（g）$是$ k_4 $ - 直径$ 3 $。 在本文中，我们证明$ |ρ（g）| \ neq 5 $，并且仅当$ g \ g \ cong j_1 \ times a $，其中$ j_1 $是第一个janko的零星简单组，而$ a $ a $ as as $ as as abelian。
Let $G$ be a finite group and let $\rm{Irr}(G)$ be the set of all irreducible complex characters of $G$. Let $\rm{cd}(G)$ be the set of all character degrees of $G$ and denote by $ρ(G)$ the set of primes which divide some character degrees in $\rm{cd}(G)$. The character graph $Δ(G)$ associated to $G$ is a graph whose vertex set is $ρ(G)$ and there is an edge between two distinct primes $p$ and $q$ if and only if the product $pq$ divides some character degree of $G$. Suppose the character graph $Δ(G)$ is $K_4$-free with diameter $3$. In this paper, we show that $|ρ(G)|\neq 5$, if and only if $G\cong J_1 \times A$, where $J_1$ is the first Janko's sporadic simple group and $A$ is abelian.
