A New Characterization of PSL(2,q) by Group Order and the Set of Vanishing Element Orders

摘要

An element g in a finite group G is called a vanishing element if there exists some irreducible complex character x of G such that y(p)=0.Denote by Vo(G)the set of orders of vanishing elements of G,and we prove that G≌PSL(2,q)if and only ifG=PSL(2,q)nd Vo(G)=Vo(PSL(2,q)),where g≥4 is a prime power.