Folner sets of alternate directed groups
[Ensembles de Folner de groupes dirigés alternés]
Brieussel, Jérémie1
1 Université Montpellier 2 Place E. Bataillon 34095 Montpellier (France)
Annales de l'Institut Fourier, Tome 64 (2014) no. 3, pp. 1109-1130.

On construit une famille explicite d’ensembles de Folner pour certains groupes dirigés agissant sur des arbres enracinés à valence sous-logarithmique par des permutations alternées. Dans le cas d’arbres à valence bornée, la moyennabilité de ces groupes avait déjà été prouvée au moyen de techniques probabilistes. La construction présentée ici fournit une nouvelle preuve, n’utilisant ni marches aléatoires, ni longueur des mots.

An explicit family of Folner sets is constructed for some directed groups acting on a rooted tree of sublogarithmic valency by alternate permutations. In the case of bounded valency, these groups were known to be amenable by probabilistic methods. The present construction provides a new and independent proof of amenability, using neither random walks, nor word length.

DOI : 10.5802/aif.2875
Classification : 20E08, 20F65, 43A00
Keywords: Groups acting on rooted trees, directed groups, bounded automata groups, Folner sets, amenability
Mot clés : groupes agissant sur des arbres enracinés, groupes dirigés, groupes d’automates bornés, ensembles de Folner, moyennabilité
Brieussel, Jérémie 1

1 Université Montpellier 2 Place E. Bataillon 34095 Montpellier (France) 
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Brieussel, Jérémie. Folner sets of alternate directed groups. Annales de l'Institut Fourier, Tome 64 (2014) no. 3, pp. 1109-1130. doi : 10.5802/aif.2875. http://www.numdam.org/articles/10.5802/aif.2875/

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