Recognition of the simple groups $PSL_2(q)$ by character degree graph and order
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2019-06-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://ijgt.ui.ac.ir/article_22212_c6dca60b79cceb6b7922abee8ca0c87c.pdf |
| Summary: | 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 $GcongPSL_2(q)$. |
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| ISSN: | 2251-7650 2251-7669 |