Bireflectionality in the commutator subgroup of a finite orthogonal group
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929626516815872 |
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| author | Nielsen, Klaus |
| author_facet | Nielsen, Klaus |
| contents | 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 $q \equiv 3 \mod 4, \dim V \equiv 2 \mod 4$ and $V$ is hyperbolic. We also classify the reversible elements of G. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bireflectionality in the commutator subgroup of a finite orthogonal group Nielsen, Klaus Group Theory 15A15, 15F10 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 $q \equiv 3 \mod 4, \dim V \equiv 2 \mod 4$ and $V$ is hyperbolic. We also classify the reversible elements of G. |
| title | Bireflectionality in the commutator subgroup of a finite orthogonal group |
| topic | Group Theory 15A15, 15F10 |
| url | https://arxiv.org/abs/2411.01323 |