On Recognizability of PSU3(q) by the Orders of Maximal Abelian Subgroups

Abstract

Li and Chen in 2012 proved that the simple group A1(pn) is uniquely determined by the set of orders of its maximal abelian subgroups. Later the authors proved that if L = A2(q), where q is not a Mersenne prime, then every finite group with the same orders of maximal abelian subgroups as L is isomorphic to L or an extension of L by a subgroup of the outer automorphism group of L. In this paper, we prove that if L = PSU3(q), where q is not a Fermat prime, then every finite group with the same set of orders of maximal abelian subgroups as L is an almost simple group with socle PSU3(q).