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

DOI: 10.2140/pjm.1973.47.5

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 Z_p × Z_p,L₂(p^m) or SL₂(p^m), where m depends on A and B. Assume G has no nontrivial solvable normal subgroup. Then G is isomorphic to Sp_n(q) or U_n(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