In this article, we consider the Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal subgroup of the orthogonal group of a non-degenerate quadratic space with a hyperbolic summand over a commutative ring, introduced by Roy. We prove a set of commutator relations among the elementary generators of the DSER elementary orthogonal group. As an application, we prove that this group is perfect and an action version of the Quillen’s local-global principle for this group is proved. This affirmatively answers a question of Rao in his Ph.D. thesis.

中文翻译：

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DSER基本正交群中换向器的瑜伽

在本文中，我们考虑由Roy引入的非退化二次空间的正交群的Dickson-Siegel-Eichler-Roy（DSER）基本正交子群，其中在交换环上具有双曲加法。我们证明了DSER基本正交群的基本生成器之间的一组换向器关系。作为一个应用，我们证明了该组是完美的，并且证明了该组的Quillen局部-全局原理的一个行动版本。肯定地回答了饶博士的问题。论文。