Groups with the same orders of maximal abelian subgroups as A₂(q)

چکیده مقاله

In Li and Chen (Sib. Math. J. 53(2), 243-247, 2012), it is proved that the simple group A₁(pⁿ) is uniquely determined by the set of orders of its maximal abelian subgroups. Let q = p^α be a prime power and L = A₂(q). In this paper, we prove that if 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. © 2013 Springer-Verlag Wien.