Recognition of the simple groups $PSL_2(q)$ by character degree graph and order
| Autor: | Zeinab Akhlaghi, Maryam Khatami, Behrooz Khosravi |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | International Journal of Group Theory, Vol 8, Iss 2, Pp 41-46 (2019) |
| Druh dokumentu: | article |
| ISSN: | 2251-7650 2251-7669 |
| DOI: | 10.22108/ijgt.2017.103226.1424 |
| Popis: | Let $G$ be a finite group, and $Irr(G)$ be the set of complex irreducible characters of $G$. Let $rho(G)$ be the set of prime divisors of character degrees of $G$. The character degree graph of $G$, which is denoted by $Delta(G)$, is a simple graph with vertex set $rho(G)$, and we join two vertices $r$ and $s$ by an edge if there exists a character degree of $G$ divisible by $rs$. In this paper, we prove that if $G$ is a finite group such that $Delta(G)=Delta(PSL_2(q))$ and $|G|=|PSL_2(q)|$, then $GcongPSL_2(q)$. |
| Databáze: | Directory of Open Access Journals |
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