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arXiv · 2409.20088

Bireflectionality in special orthogonal groups

Klaus Nielsen
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Abstract

It is shown that a transformation in the special orthogonal group SO(V) of a nondefective quadratic space over a field K is bireflectional (product of 2 involutions) if and only if it is reversible (conjugate to its inverse). Furthermore, all elements of SO(V) are bireflectional if and only if dim V is odd or divisible by 4, or V is a hyperbolic plane over GF(2) or GF(3).

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Klaus Nielsen. 2024-09-30. Bireflectionality in special orthogonal groups. https://arxiv.org/abs/2409.20088

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