Roy初等正交群的正规性与$K_1$ -稳定性
Normality and $K_1$-stability of Roy's elementary orthogonal group
摘要：
本文证明了交换环上Roy初等正交群（Dickson-Siegel-Eichler-Roy或DSER群）的正规性。Roy在[MR 0231844]中在双曲秩的某些条件下。我们还建立了Roy群的$K_1$的稳定性定理。我们得到了初等正交群的一个分解定理，并利用它导出了稳定性定理。
英文摘要：
In this paper, we prove the normality of the Roy's elementary orthogonal group (Dickson--Siegel--Eichler--Roy or DSER group) over a commutative ring which was introduced by A. Roy in [MR0231844] under some conditions on the hyperbolic rank. We also establish a stability theorem for $K_1$ of Roy's group. We obtain a decomposition theorem for the elementary orthogonal group which is used to deduce the stability theorem.
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