Normality of DSER elementary orthogonal group

2017/03/12 by Ambily, A. A., Rao, Ravi A. · 1 citation
#19B99 #19G99 (primary) #20G35 #20H25 (secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1703.04083

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 EO_R(Q, H(R)^m) of the orthogonal group O_R(Q ⊥ H(R)^m), with rank Q= n ≥ 1 and m≥ 2. We show that EO_R(Q, H(R)^m) is a normal subgroup of O_R(Q ⊥ H(R)^m), for all m≥ 2. We also prove that the DSER group EO_R(Q, H(P)) is a normal subgroup of O_R(Q ⊥ H(P)), where Q and H(P) are quadratic spaces over a commutative ring R, with rank (Q) ≥ 1 and rank (P) ≥ 2.

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• Horrocks theorem for odd orthogonal groups

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