Bireflectionality in the commutator subgroup of a finite orthogonal group
Group Theory
2024-12-13 v2
Abstract
We classify the bireflections (products of 2 involutions) in the commutator subgroup G an orthogonal group O(V) over a finite field GF(q) of characteristic not 2. We show that every element of G is a bireflection if it is reversible (conjugate to its inverse in G), except when and is hyperbolic. We also classify the reversible elements of G.
Cite
@article{arxiv.2411.01323,
title = {Bireflectionality in the commutator subgroup of a finite orthogonal group},
author = {Klaus Nielsen},
journal= {arXiv preprint arXiv:2411.01323},
year = {2024}
}
Comments
11 pages. Corrected an obvious error in remark 3.1. Corrected argument in the proof of lemma 3.10