On the Isomorphisms between Certain Congruence Groups

Abstract

In this paper we study the possible isomorphisms between the congruence subgroups of the classical groups over integral domains by applying the involution-free techniques previously used by O’Meara and the author. We prove, in dimensions at least 6 and characteristic not 2, that a linear congruence group is never isomorphic to a symplectic congruence group nor to an isotropic unitary congruence group whose associated hermitian space has Witt index at least 3.