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Recognition of the simple groups $PSL_2(q)$ by character degree graph and order | ||
| International Journal of Group Theory | ||
| مقاله 11، دوره 8، شماره 2، شهریور 2019، صفحه 41-46 اصل مقاله (193.8 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2017.103226.1424 | ||
| نویسندگان | ||
| Zeinab Akhlaghi1؛ Maryam Khatami* ؛ Behrooz Khosravi2 | ||
| 1Faculty of Mathematics and Computer science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran | ||
| 2Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran | ||
| چکیده | ||
| 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 $G\cong PSL_2(q)$. | ||
| کلیدواژهها | ||
| character degree graph؛ simple group؛ characterization | ||
| مراجع | ||
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