Bireflectionality in special orthogonal groups
Group Theory
2024-10-01 v1
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).
Keywords
Cite
@article{arxiv.2409.20088,
title = {Bireflectionality in special orthogonal groups},
author = {Klaus Nielsen},
journal= {arXiv preprint arXiv:2409.20088},
year = {2024}
}
Comments
11 pages