English

Normality of DSER elementary orthogonal group

Commutative Algebra 2017-03-17 v1 K-Theory and Homology

Abstract

Let (Q,q)(Q, q) be a quadratic space over a commutative ring RR in which 22 is invertible, and consider the Dickson--Siegel--Eichler--Roy's subgroup EOR(Q,H(R)m)EO_{R}(Q, H(R)^{m}) of the orthogonal group OR(QH(R)m)O_R(Q \perp H(R)^m), with rank Q=n1Q= n \geq 1 and m2m\geq 2. We show that EOR(Q,H(R)m)EO_{R}(Q, H(R)^{m}) is a normal subgroup of OR(QH(R)m)O_R(Q \perp H(R)^m), for all m2m\geq 2. We also prove that the DSER group EOR(Q,H(P))EO_{R}(Q, H(P)) is a normal subgroup of OR(QH(P))O_{R}(Q \perp H(P)), where QQ and H(P)H(P) are quadratic spaces over a commutative ring RR, with rank (Q)1(Q) \ge 1 and rank (P)2(P) \ge 2.

Cite

@article{arxiv.1703.04083,
  title  = {Normality of DSER elementary orthogonal group},
  author = {A. A. Ambily and Ravi A. Rao},
  journal= {arXiv preprint arXiv:1703.04083},
  year   = {2017}
}

Comments

11 pages

R2 v1 2026-06-22T18:43:22.896Z