Cayley-Abels graphs and invariants of totally disconnected, locally compact groups
| Autor: | ARNBJÖRG SOFFÍA ÁRNADÓTTIR, WALTRAUD LEDERLE, RÖGNVALDUR G. MÖLLER |
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| Přispěvatelé: | UCL - SST/IRMP - Institut de recherche en mathématique et physique |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
modular function
General Mathematics scale function ComputingMethodologies_DOCUMENTANDTEXTPROCESSING FOS: Mathematics 22D05 (Primary) 05C25 20B27 20E08 (Secondary) Totally disconnected locally compact groups Group Theory (math.GR) Mathematics - Group Theory Cayley-Abels graphs groups acting on trees |
| Zdroj: | Australian Mathematical Society. Journal, Vol. np, no.np, p. 1-33 (2022) |
| ISSN: | 1446-7887 |
| Popis: | A connected, locally finite graph $\Gamma $ is a Cayley–Abels graph for a totally disconnected, locally compact group G if G acts vertex-transitively on $\Gamma $ with compact, open vertex stabilizers. Define the minimal degree of G as the minimal degree of a Cayley–Abels graph of G. We relate the minimal degree in various ways to the modular function, the scale function and the structure of compact open subgroups. As an application, we prove that if $T_{d}$ denotes the d-regular tree, then the minimal degree of $\mathrm{Aut}(T_{d})$ is d for all $d\geq 2$ . |
| Databáze: | OpenAIRE |
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