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).