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Keywords:
finite non-Abelian simple group; irreducible complex character; character-prime graph
finite non-Abelian simple group; irreducible complex character; character-prime graph
Summary:
Let $G$ be a finite group and ${\rm Irr}(G)$ the set of all irreducible complex characters of $G$. Let ${\rm cd} (G)$ be the set of all irreducible complex character degrees of $G$ and denote by $\rho (G)$ the set of all primes which divide a character degree of $G$. The character-prime graph $\Gamma (G)$ associated to $G$ is a simple undirected graph whose vertex set is $\rho (G)$ and there is an edge between two distinct primes $p$ and $q$ if and only if the $pq$ divides a character degree of $G$. We show that the finite non-Abelian simple group $U_{3}(7)$, $M_{11}$, $L_{2}(16)$, $L_{2}(25)$, $L_{2}(81)$, $U_{3}(8)$, $U_{3}(9)$, $Sz(8)$, $Sz(32)$ and $L_{2}(p)$ are uniquely determined by their degree-patterns and orders.
References:
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