Recognition of the simple groups $PSL_2(q)$ by character degree graph and order
نویسندگان
1 Assistant Professor, Department of General Medicine, PSG Institute of Medical Science and Research
2 Assistant Professor, Department of General Medicine, PSG Institute of Medical Science and Research
3 Assistant Professor, Department of General Medicine, PSG Institute of Medical Science and Research
4 Associate Professor, Department of General Medicine, PSG Institute of Medical Science and Research
5 Assistant Professor, Department of General Medicine, PSG Institute of Medical Science and Research
6 Professor, Department of General Medicine, PSG Institute of Medical Science and Research
doi
10.22108/ijgt.2017.103226.1424چکیده
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 $G\cong PSL_2(q)$.
