Powers of commutators in linear algebraic groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866915025222893568 |
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| author | Martin, Benjamin |
| author_facet | Martin, Benjamin |
| contents | Let ${\mathscr G}$ be a linear algebraic group over $k$, where $k$ is an algebraically closed field, a pseudo-finite field or the valuation ring of a nonarchimedean local field. Let $G= {\mathscr G}(k)$. We prove that if $γ, δ\in G$ such that $γ$ is a commutator and $\langle δ\rangle= \langle γ\rangle$ then $δ$ is a commutator. This generalises a result of Honda for finite groups. Our proof uses the Lefschetz Principle from first-order model theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13037 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Powers of commutators in linear algebraic groups Martin, Benjamin Group Theory 20G15 (20F12, 03C98) Let ${\mathscr G}$ be a linear algebraic group over $k$, where $k$ is an algebraically closed field, a pseudo-finite field or the valuation ring of a nonarchimedean local field. Let $G= {\mathscr G}(k)$. We prove that if $γ, δ\in G$ such that $γ$ is a commutator and $\langle δ\rangle= \langle γ\rangle$ then $δ$ is a commutator. This generalises a result of Honda for finite groups. Our proof uses the Lefschetz Principle from first-order model theory. |
| title | Powers of commutators in linear algebraic groups |
| topic | Group Theory 20G15 (20F12, 03C98) |
| url | https://arxiv.org/abs/2209.13037 |