On Recognizability of PSU ₃ (q) by the Orders of Maximal Abelian Subgroups

چکیده مقاله

Li and Chen in 2012 proved that the simple group A ₁ (p ⁿ ) is uniquely determined by the set of orders of its maximal abelian subgroups. Later the authors proved that if L = A ₂ (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 = PSU ₃ (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 PSU ₃ (q). © 2019, Pleiades Publishing, Ltd.