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arXiv · 2503.12839

Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group

Gayathry Pradeep·Ambily Ambattu Asokan·Aparna Pradeep Vadakke Kovilakam
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Abstract

We prove the Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group, which was introduced by Amit Roy in 1968 and the Eichler-Siegel-Dickson transvection group, which is in literature in the works of Dickson, Siegel and Eichler, are equal over a commutative ring in which $2$ is invertible. We prove the equality in the free case by considering the odd and even case separately and then generalize this result by using the local-global principle. This result generalizes previous results concerning the equality of elementary orthogonal transvection groups.

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Gayathry Pradeep, Ambily Ambattu Asokan, Aparna Pradeep Vadakke Kovilakam. 2025-03-17. Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group. https://arxiv.org/abs/2503.12839

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