Normal Structure of Isotropic Odd Orthogonal Groups

Leonid Danilevich

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arXiv · 2601.00763

Normal Structure of Isotropic Odd Orthogonal Groups

Leonid Danilevich

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Abstract

Let $(M, q)$ be a quadratic projective module of an odd rank over an commutative ring, where the form $q$ is semiregular, with global Witt index of at least $2$, and with $\mathrm{rk}(M) \ge 7$. We prove standard commutator formulae and classify $\mathrm{EO}$-normal subgroups of $\mathrm{O}(M, q)$ without assumption of $2$ being invertible.

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Leonid Danilevich. 2026-01-02. Normal Structure of Isotropic Odd Orthogonal Groups. https://arxiv.org/abs/2601.00763

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