Quasirecognition of e 6 (q) by the orders of maximal abelian subgroups

چکیده مقاله

In [Li and Chen, A new characterization of the simple group A1(pn), Sib. Math. J. 53(2) (2012) 213-247.], it is proved that the simple group A1(pn) is uniquely determined by the set of orders of its maximal abelian subgroups. Also in [Momen and Khosravi, Groups with the same orders of maximal abelian subgroups as A2(q), Monatsh. Math. 174 (2013) 285-303], 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 G is a finite group with the same orders of maximal abelian subgroups as E6(q), then G has a unique nonabelian composition factor which is isomorphic to E6(q). © 2018 World Scientific Publishing Company.