Bireflectionality in special orthogonal groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909330456969216 |
|---|---|
| author | Nielsen, Klaus |
| author_facet | Nielsen, Klaus |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bireflectionality in special orthogonal groups Nielsen, Klaus Group Theory 15A15, 15F10 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). |
| title | Bireflectionality in special orthogonal groups |
| topic | Group Theory 15A15, 15F10 |
| url | https://arxiv.org/abs/2409.20088 |