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- Title
Quasirecognition of E6(q) by the orders of maximal abelian subgroups.
- Authors
Momen, Zahra; Khosravi, Behrooz
- Abstract
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).
- Subjects
FINITE simple groups; ABELIAN groups; MAXIMAL subgroups; AUTOMORPHISM groups; NONABELIAN groups
- Publication
Journal of Algebra & Its Applications, 2018, Vol 17, Issue 7, pN.PAG
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498818501220