Let K be a quadratic extension of a global field F, of characteristic not t
wo, and O-S the integral closure in K of a Dedekind ring of S-integers D-S
in F. Then PSL(2, O-S) is isomorphic to the spinorial kernel O'(L) for an i
ndefinite quadratic D-S-lattice L of rank 4. The isomorphism is used to stu
dy the conjugacy classes of unitary groups PSU(h, O-S) of primitive odd bin
ary hermitian matrices h under the action of PSL(2, O-S).