Fixed point groups of involutions of type $\mathrm{O}(\mathrm{q},k)$ over a field of characteristic two

Mark Hunnell; John Hutchens

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arXiv · 2301.05887

Fixed point groups of involutions of type $\mathrm{O}(\mathrm{q},k)$ over a field of characteristic two

Mark Hunnell·John Hutchens

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Abstract

For $\mathrm{O}(\mathrm{q},k)$, the orthogonal group over a field $k$ of characteristic 2 with respect to a quadratic form $\mathrm{q}$, we discuss the isomorphism classes of fixed points of involutions. When the quadratic space is either totally singular or nonsingular, a full classification of the isomorphism classes is given. We also give some implications of these results for a general quadratic space over a field of characteristic $2$.

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Mark Hunnell, John Hutchens. 2023-01-14. Fixed point groups of involutions of type $\mathrm{O}(\mathrm{q},k)$ over a field of characteristic two. https://arxiv.org/abs/2301.05887

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