Subnormal structure of non-stable unitary groups over rings

Let R be a commutative ring with identity in which 2 is invertible. Let H denote a subgroup of the unitary group U (2 n, R, Λ) with n ≥ 4. H is normalized by E U (2 n, J, Γ^J) for some form ideal (J, Γ^J) of the form ring (R, Λ). The purpose of the paper is to prove that H satisfies a "sandwich" property, i.e. there exists a form ideal (I, Γ^I) such that E U (2 n, I J⁸ Γ^J, Γ) ⊆ H ⊆ C U (2 n, I, Γ^I) . Furthermore, we give a classification for the subnormal subgroups of the unitary group U (2 n, R, Λ), which is an analog for the results existing in the general linear groups; see [L.N. Vaserstein, The subnormal structure of general linear groups over rings, Math. Proc. Cambridge Philos. Soc., 108 (1990) 219-229; N.A. Vavilov, Subnormal structure of general linear group, Math. Proc. Cambridge Philos. Soc. 107 (1990) 103-106; J.S. Wilson, The normal and subnormal structure of general linear groups, Proc. Cambridge Philos. Soc. 71 (1972) 163-177].