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arXiv · 2405.13603

On the number of generators of groups acting arc-transitively on graphs

Marco Barbieri·Pablo Spiga
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Abstract

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.

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Marco Barbieri, Pablo Spiga. 2024-05-22. On the number of generators of groups acting arc-transitively on graphs. https://arxiv.org/abs/2405.13603

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