Article
| Title: | A new characterization of non-Abelian simple groups by their degree-patterns and orders (English) |
| Author: | Tao, Shijie |
| Author: | Wang, Qianqian |
| Author: | Shao, Changguo |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 1 |
| Year: | 2026 |
| Pages: | 31-38 |
| Summary lang: | English |
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| Category: | math |
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| 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. (English) |
| Keyword: | finite non-Abelian simple group |
| Keyword: | irreducible complex character |
| Keyword: | character-prime graph |
| MSC: | 05C25 |
| MSC: | 20C15 |
| DOI: | 10.21136/CMJ.2026.0061-25 |
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| Date available: | 2026-03-13T09:27:33Z |
| Last updated: | 2026-03-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153558 |
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