Stable sandwich classification theorem for classical-like groups

Let H denote a subgroup of the unitary group U(R, Λ) which is normalized by EU(J, Γ^J) for some form ideal (J, Γ^J) of a commutative form ring (R, Λ). We prove that H satisfies a "sandwich" property, i.e., there exists a form ideal (I, Γ^I) such that EU(I, Γ^I) ⊆ H ⊆ U(I: J⁷, Ω) for some form ideal (I: J⁷, Ω). This answers a conjecture of Bak (1967) in the stable case.