Proves solvability in the SK 1-analog of orthogonal groups, suggesting a strong connection between local and global properties.
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 SK 1 -analog of the orthogonal groups and study the homotopy and commutativity principle for odd elementary orthogonal groups.
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Ambily et al. (2026) studied this question.
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