A new characterization for some linear groups

Abstract

Let G be a group and πe(G) be the set of element orders of G. Let ε πe(G) and mk be the number of elements of order k in G. Let nse(G) = {mk εe(G). In Shen et al. (Monatsh Math, 2009), the authors proved that A4 ≅ PSL(2,3), A5 ≅ PSL(2,4) ≅ PSL(2,5) and A6 ≅ PSL(2,9) are uniquely determined by nse(G). In this paper, we prove that if G is a group such that nse(G) = nse(PSL(2, q)), where q ε {7,8,11,13}, then G ≅ PSL(2,q). © 2009 Springer-Verlag.