On the number of generators of groups acting arc-transitively on graphs
Abstract
Given a finite connected graph ${\Gamma}$ and a group $G$ acting transitively on the vertices of ${\Gamma}$, we prove that the number of vertices of ${\Gamma}$ and the cardinality of $G$ are bounded above by a function depending only on the cardinality of ${\Gamma}$ 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 ${\Gamma}$ cannot be bounded by a function of the valency alone.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.13603
- arXiv:
- arXiv:2405.13603
- Bibcode:
- 2024arXiv240513603B
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Combinatorics;
- 20B25;
- 05C25