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In this paper, we prove the normality of the Roy's elementary orthogonalgroup (Dickson--Siegel--Eichler--Roy or DSER group) over a commutative ringwhich was introduced by A. Roy in [MR0231844] under some conditions on thehyperbolic rank. We also establish a stability theorem for $K_1$ of Roy'sgroup. We obtain a decomposition theorem for the elementary orthogonal groupwhich is used to deduce the stability theorem.

Normality and $K_1$-stability of Roy's elementary orthogonal group