On the number of generators of groups acting arc-transitively on graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913617564139520 |
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| author | Barbieri, Marco Spiga, Pablo |
| author_facet | Barbieri, Marco Spiga, Pablo |
| contents | Given a finite connected graph $Γ$ and a group $G$ acting transitively on the vertices of $Γ$, we prove that the number of vertices of $Γ$ and the cardinality of $G$ are bounded above by a function depending only on the cardinality of $Γ$ and on the exponent of $G$. We also prove that the number of generators of a group $G$ acting transitively on the arcs of a finite graph $Γ$ cannot be bounded by a function of the valency alone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the number of generators of groups acting arc-transitively on graphs Barbieri, Marco Spiga, Pablo Group Theory Combinatorics 20B25, 05C25 Given a finite connected graph $Γ$ and a group $G$ acting transitively on the vertices of $Γ$, we prove that the number of vertices of $Γ$ and the cardinality of $G$ are bounded above by a function depending only on the cardinality of $Γ$ and on the exponent of $G$. We also prove that the number of generators of a group $G$ acting transitively on the arcs of a finite graph $Γ$ cannot be bounded by a function of the valency alone. |
| title | On the number of generators of groups acting arc-transitively on graphs |
| topic | Group Theory Combinatorics 20B25, 05C25 |
| url | https://arxiv.org/abs/2405.13603 |