Automorphism Orbits of the Group of Unitriangular Matrices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917003137122304 |
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| author | de Melo, Emerson Kato, Júlia |
| author_facet | de Melo, Emerson Kato, Júlia |
| contents | Let $G$ be a group. The orbits of the natural action of $Aut(G)$ on $G$ are called the automorphism orbits of $G$, and their number is denoted by $ω(G)$. Let $\mathbb{F}$ be an infinite field, and let $UT_n(\mathbb{F})$ denote the group of unitriangular matrices over $\mathbb{F}$. We show that $ω(UT_n(\mathbb{F}))$ is finite for $n \leq 5$ and infinite for $n \geq 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automorphism Orbits of the Group of Unitriangular Matrices de Melo, Emerson Kato, Júlia Group Theory Let $G$ be a group. The orbits of the natural action of $Aut(G)$ on $G$ are called the automorphism orbits of $G$, and their number is denoted by $ω(G)$. Let $\mathbb{F}$ be an infinite field, and let $UT_n(\mathbb{F})$ denote the group of unitriangular matrices over $\mathbb{F}$. We show that $ω(UT_n(\mathbb{F}))$ is finite for $n \leq 5$ and infinite for $n \geq 6$. |
| title | Automorphism Orbits of the Group of Unitriangular Matrices |
| topic | Group Theory |
| url | https://arxiv.org/abs/2510.09353 |