On the non-discreteness of automorphism groups of Cayley graphs of Coxeter groups

2023/02/09 by Federico Berlai, Berlai, Federico, Michal Ferov +1
Computer Science · Materials Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Nanocluster Synthesis and Applications #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2302.04444

openalex publication_date 2023/02/09 · openalex created_date 2023/02/13 · openalex updated_date 2026/07/28

Abstract

In this work we characterise Cayley graphs of Coxeter groups with respect to the standard generating set that admit uncountable vertex stabilisers. As a corollary, we fully identify finitely generated Coxeter groups for which the automorphism group of their Cayley graph with respect to the standard generating set is not discrete when equipped with the permutation topology. As an application, we also provide new explicit constructions of vertex-transitive graphs of infinite degree that have locally compact automorphism groups.

Related

• Automorphisms of geometric structures associated to Coxeter groups
• Automorphisms of Cayley graphs on generalised dicyclic groups
• Automorphism groups of graphs
• Cayley properties of merged Johnson graphs
• Cayley graphs on abelian groups