On Recognizability of PSU3(q) by the Orders of Maximal Abelian Subgroups
- 2 Downloads
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).
Keywordssimple group maximal abelian subgroup characterization projective special unitary group prime graph
Unable to display preview. Download preview PDF.
- 5.Wang L., Characterization of Some Classes of Finite Simple Groups, Thes. Master of Science, Southwest China Normal University (2000).Google Scholar
- 32.King O. H., “The subgroup structure of finite classical groups in terms of geometric configurations,” in: Surv. Comb., London Math. Soc., 2005) (Lect. Note Ser.; vol. 327, 29–56.Google Scholar