Normality theorem for elementary symplectic groups

A. A. Suslin proved a normality theorem for an elementary linear group, which says that an elementary linear group of size bigger than or equal to [Formula: see text] over a commutative ring with unity is normal in the general linear group of the same size. Subsequently, V. I. Kopeiko extended this result of Suslin for a symplectic group defined with respect to the standard skew-symmetric matrix of even size. Here we generalize the result of Kopeiko for a symplectic group defined with respect to any invertible skew-symmetric matrix of Pfaffian one.