Normality of DSER elementary orthogonal group

Abstract

Let $(Q,q)$ be a quadratic space over a commutative ring $R$ in which $2$ is invertible, and consider the Dickson--Siegel--Eichler--Roy's subgroup $E{O}_R(Q,H(R{)}^m)$ of the orthogonal group $O_R(Q\perp H(R{)}^m)$, with rank $Q=n\ge 1$ and $m\ge 2$. We show that $E{O}_R(Q,H(R{)}^m)$ is a normal subgroup of $O_R(Q\perp H(R{)}^m)$, for all $m\ge 2$. We also prove that the DSER group $E{O}_R(Q,H(P))$ is a normal subgroup of $O_R(Q\perp H(P))$, where $Q$ and $H(P)$ are quadratic spaces over a commutative ring $R$, with rank $(Q)\ge 1$ and rank $(P)\ge 2$.

11 pages

References in corpus (1)

• Yoga of Commutators in Roy's Elementary Orthogonal Group