TY - JOUR
ID - 22212
TI - Recognition of the simple groups $PSL_2(q)$ by character degree graph and order
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Akhlaghi, Zeinab
AU - Khatami, Maryam
AU - Khosravi, Behrooz
AD - Faculty of Mathematics and Computer science, Amirkabir University of Technology (Tehran
Polytechnic), Tehran, Iran
AD -
AD - Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran
Polytechnic), 15914 Tehran, Iran
Y1 - 2019
PY - 2019
VL - 8
IS - 2
SP - 41
EP - 46
KW - character degree graph
KW - simple group
KW - characterization
DO - 10.22108/ijgt.2017.103226.1424
N2 - 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 $G\cong PSL_2(q)$.
UR - https://ijgt.ui.ac.ir/article_22212.html
L1 - https://ijgt.ui.ac.ir/article_22212_c6dca60b79cceb6b7922abee8ca0c87c.pdf
ER -