Amenable, transitive and faithful actions of groups acting on trees

Pierre Fima[1]

  • [1] Université Denis-Diderot Paris 7, IMJ, Bâtiment Sophie Germain, case 7012, 75205 Paris cedex 13

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 1, page 1-17
  • ISSN: 0373-0956

Abstract

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We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.

How to cite

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Fima, Pierre. "Amenable, transitive and faithful actions of groups acting on trees." Annales de l’institut Fourier 64.1 (2014): 1-17. <http://eudml.org/doc/275431>.

@article{Fima2014,
abstract = {We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.},
affiliation = {Université Denis-Diderot Paris 7, IMJ, Bâtiment Sophie Germain, case 7012, 75205 Paris cedex 13},
author = {Fima, Pierre},
journal = {Annales de l’institut Fourier},
keywords = {amenable action; free product; HNN extension; groups acting on trees},
language = {eng},
number = {1},
pages = {1-17},
publisher = {Association des Annales de l’institut Fourier},
title = {Amenable, transitive and faithful actions of groups acting on trees},
url = {http://eudml.org/doc/275431},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Fima, Pierre
TI - Amenable, transitive and faithful actions of groups acting on trees
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 1
SP - 1
EP - 17
AB - We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.
LA - eng
KW - amenable action; free product; HNN extension; groups acting on trees
UR - http://eudml.org/doc/275431
ER -

References

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  9. S. Moon, Permanent properties of amenable, transitive and faithful actions, Bull. Belgian Math. Soc. Simon Stevin 18 (2011), 287-296 Zbl1221.43002MR2848804
  10. J.-P. Serre, Arbres, amalgames, SL 2 , 46 (1983) Zbl0369.20013
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  13. R. J. Zimmer, Ergodic theory and semisimple groups,, (1984), Birkhäuser, Basel Zbl0571.58015MR776417

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