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A characterization of the unitary and symplectic groups over finite fields of characteristic at least $5$

Aschbacher, Michael (1973) A characterization of the unitary and symplectic groups over finite fields of characteristic at least $5$. Pacific Journal of Mathematics, 47 (1). pp. 5-26. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:ASCpjm73

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Abstract

The following characterization is obtained: THEOREM. Let G be a finite group generated by a conjugacy class D of subgroups of prime order p ^ 5, such that for any choice of distinct A and B in D, the subgroup generated by A and B is isomorphic to Zp x Zp, L2(pm) or SL2(pm), where m depends on A and B. Assume G has no nontrivial solvable normal subgroup. Then G is isomorphic to Spn(q) or Un(q) for some power q of p.


Item Type:Article
Additional Information:Received February 25, 1972 and in revised form February 26, 1973. Euclid Identifier: euclid.pjm/1102946071 Zentralblatt Math Identifier : 0299.20009 Mathmatical Reviews number (MathSciNet): MR0338151
Record Number:CaltechAUTHORS:ASCpjm73
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:ASCpjm73
Alternative URL:http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.pjm/1102946071
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ID Code:542
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:14 Jul 2005
Last Modified:26 Dec 2012 08:40

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