Title of article :
RECOGNITION OF THE SIMPLE GROUPS PSL2(q) BY CHARACTER DEGREE GRAPH and ORDER
Author/Authors :
AKHLAGHI, ZEINAB Faculty of Mathematics and Computer science - Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran , KHATAMI, MARYAM Faculty of Mathematics and Computer Science - Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran , KHOSRAVI, BEHROOZ Faculty of Mathematics and Computer Science - Amirkabir University of Technology (Tehran Polytechnic), 15914 Tehran, Iran
Abstract :
Abstract. Let G be a nite group, and Irr(G) be the set of complex irreducible characters of G. Let
p(G) be the set of prime divisors of character degrees of G. The character degree graph of G, which is
denoted by Δ(G), is a simple graph with vertex set p(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 nite group such
that Δ(G) = Δ(PSL2(q)) and /G/ = /PSL2(q)/, then G≅PSL2(q).
Keywords :
characterization , simple group , character degree graph
