Bireflections of the commutator subgroup of an orthogonal group over the reals
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912152209588224 |
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| author | Nielsen, Klaus |
| author_facet | Nielsen, Klaus |
| contents | Let $O(p,q)$ be the orthogonal groups of signature $(p,q)$ over the reals. It is shown that an element of the commutator subgroup $O(p,q)'$ of $O(p,q)$ is bireflectional (product of 2 involutions in $O(p,q)'$) if and only if it is reversible (conjugate to its inverse). Moreover, the bireflectional elements of $O(p, q)'$ are classified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bireflections of the commutator subgroup of an orthogonal group over the reals Nielsen, Klaus Group Theory 20G20, 14L35, 15A23 Let $O(p,q)$ be the orthogonal groups of signature $(p,q)$ over the reals. It is shown that an element of the commutator subgroup $O(p,q)'$ of $O(p,q)$ is bireflectional (product of 2 involutions in $O(p,q)'$) if and only if it is reversible (conjugate to its inverse). Moreover, the bireflectional elements of $O(p, q)'$ are classified. |
| title | Bireflections of the commutator subgroup of an orthogonal group over the reals |
| topic | Group Theory 20G20, 14L35, 15A23 |
| url | https://arxiv.org/abs/2412.08253 |