Four-dimensional symplectic groups

Abstract

In R. E. Solazzi, J. Algebra 21 (1972), 91–102 , the automorphisms of the symplectic congruence groups and their corresponding projective groups were found over any integral domain, in dimensions greater than four. The purpose of this paper is to determine these automorphisms in dimension four. In characteristic not 2 the automorphisms of the projective congruence groups have the same characterization as in the previous paper; they are determined by transformation by a symplectic semisimilitude. This is Theorem 2.5. The remaining sections of this paper deal with exceptional automorphisms of the congruence groups that do not preserve transvections and which can occur with four-dimensional congruence groups in characteristic 2.