PUB - Publikationen an der Universität Bielefeld

In this paper we define odd dimensional unitary groups U2n+1 (R, Delta). These groups contain as special cases the odd dimensional general linear groups GL(2n+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 U-2n (R, Delta) where (R, Delta) is any form ring. We classify the E-normal subgroups of the groups U2n+1(R, Delta) (i.e. the subgroups which are normalized by the elementary subgroup EU2n+1 (R, Delta)), 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, Delta) by conjugation on the set of all E-normal subgroups. (C) 2017 Elsevier B.V. All rights reserved.