A new characterization of non-Abelian simple groups by their degree-patterns and orders
Abstract
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.
Fields of Study & Subjects
Finite Group Theory Research
Graph theory and applications
Advanced Algebra and Geometry
Publication details
- Journal / source
- Czechoslovak Mathematical Journal
- Volume
- 76
- Issue
- 1
- Pages
- 31–38
- Publication date
- 19 January 2026
- Language
- EN