The E-normal structure of odd dimensional unitary groups

In this paper we define odd dimensional unitary groups U2n+1(R,Δ). These groups contain as special cases the odd dimensional general linear groups GL2n+1(R) where R is any ring, the odd dimensional orthogonal and symplectic groups O2n+1(R) and Sp2n+1(R) where R is any commutative ring and further the first author's even dimensional unitary groups U2n(R,Λ) where (R,Λ) is any form ring. We classify the E-normal subgroups of the groups U2n+1(R,Δ) (i.e. the subgroups which are normalized by the elementary subgroup EU2n+1(R,Δ)), under the condition that R is either a semilocal or quasifinite ring with involution and n≥3. Further we investigate the action of U2n+1(R,Δ) by conjugation on the set of all E-normal subgroups.