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arXiv · 2504.16509

Solvability of the ${\rm SK}_1$-analog of the orthogonal groups

Ambily A. A.·Gayathry Pradeep
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Abstract

We prove the dilation principle for the relative Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group and using the dilation principle we prove the Quillen's analog of the local-global principle for the group. Applying the relative local-global principle, we prove the solvability and nilpotency of the ${\rm SK_1}$-analog of the orthogonal groups and study the homotopy and commutativity principle for odd elementary orthogonal groups.

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Ambily A. A., Gayathry Pradeep. 2025-04-23. Solvability of the ${\rm SK}_1$-analog of the orthogonal groups. https://arxiv.org/abs/2504.16509

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