Vol. 47, No. 1, 1973

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

Michael Aschbacher

Vol. 47 (1973), No. 1, 5–26
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 × 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.

Mathematical Subject Classification 2000
Primary: 20D05
Milestones
Received: 25 February 1972
Revised: 26 February 1973
Published: 1 July 1973
Authors
Michael Aschbacher