Normality and K1K1-stability of Roy's elementary orthogonal group

In this paper, we prove the normality of the elementary orthogonal group (Dickson–Siegel–Eichler–Roy or DSER group) over a commutative ring which was introduced by A. Roy in [14] under some conditions on the hyperbolic rank. We also establish stability theorems for K1K1 of Roy's group under different stable range conditions. We obtain a decomposition theorem for the elementary orthogonal group which is used to deduce the stability theorem.