Folner sets of alternate directed groups

Jérémie Brieussel[1]

  • [1] Université Montpellier 2 Place E. Bataillon 34095 Montpellier (France)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 3, page 1109-1130
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Brieussel, Jérémie. "Folner sets of alternate directed groups." Annales de l’institut Fourier 64.3 (2014): 1109-1130. <http://eudml.org/doc/275492>.

@article{Brieussel2014,
abstract = {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.},
affiliation = {Université Montpellier 2 Place E. Bataillon 34095 Montpellier (France)},
author = {Brieussel, Jérémie},
journal = {Annales de l’institut Fourier},
keywords = {Groups acting on rooted trees; directed groups; bounded automata groups; Folner sets; amenability; rooted trees},
language = {eng},
number = {3},
pages = {1109-1130},
publisher = {Association des Annales de l’institut Fourier},
title = {Folner sets of alternate directed groups},
url = {http://eudml.org/doc/275492},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Brieussel, Jérémie
TI - Folner sets of alternate directed groups
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 3
SP - 1109
EP - 1130
AB - 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.
LA - eng
KW - Groups acting on rooted trees; directed groups; bounded automata groups; Folner sets; amenability; rooted trees
UR - http://eudml.org/doc/275492
ER -

References

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