Cayley graphs with few automorphisms: the case of infinite groups
Group Theory
2024-03-21 v2 Combinatorics
Abstract
We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every finitely generated group admits a Cayley graph with countable automorphism group. We also treat the case of directed graphs.
Keywords
Cite
@article{arxiv.2010.06020,
title = {Cayley graphs with few automorphisms: the case of infinite groups},
author = {Paul-Henry Leemann and Mikael de la Salle},
journal= {arXiv preprint arXiv:2010.06020},
year = {2024}
}
Comments
v1: 17 pages v2: 19 pages, improvements in the presentation, Section 6 added. To appear in Annales Henri Lebesgue