Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property

Soyoung Moon[1]

  • [1] Institut de Mathématiques Université de Bourgogne UMR 5584 du CNRS 9 avenue Alain Savary - BP 47870 21078 Dijon cedex France

Annales mathématiques Blaise Pascal (2011)

  • Volume: 18, Issue: 2, page 211-229
  • ISSN: 1259-1734

Abstract

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We show that the amalgamated free products of two free groups over a cyclic subgroup admit amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on two generators.

How to cite

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Moon, Soyoung. "Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property." Annales mathématiques Blaise Pascal 18.2 (2011): 211-229. <http://eudml.org/doc/219809>.

@article{Moon2011,
abstract = {We show that the amalgamated free products of two free groups over a cyclic subgroup admit amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on two generators.},
affiliation = {Institut de Mathématiques Université de Bourgogne UMR 5584 du CNRS 9 avenue Alain Savary - BP 47870 21078 Dijon cedex France},
author = {Moon, Soyoung},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Amenable actions; amalgamated free products; Baire’s property; Følner sequence; amenable action; amalgamated free product of free groups},
language = {eng},
month = {7},
number = {2},
pages = {211-229},
publisher = {Annales mathématiques Blaise Pascal},
title = {Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property},
url = {http://eudml.org/doc/219809},
volume = {18},
year = {2011},
}

TY - JOUR
AU - Moon, Soyoung
TI - Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property
JO - Annales mathématiques Blaise Pascal
DA - 2011/7//
PB - Annales mathématiques Blaise Pascal
VL - 18
IS - 2
SP - 211
EP - 229
AB - We show that the amalgamated free products of two free groups over a cyclic subgroup admit amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on two generators.
LA - eng
KW - Amenable actions; amalgamated free products; Baire’s property; Følner sequence; amenable action; amalgamated free product of free groups
UR - http://eudml.org/doc/219809
ER -

References

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  1. Eric K. van Douwen, Measures invariant under actions of F 2 , Topology Appl. 34 (1990), 53-68 Zbl0701.43001MR1035460
  2. B. Fine, G. Rosenberger, Algebraic generalizations of discret groups, (1999), Marcel Dekker, Inc. Zbl0933.20001MR1712997
  3. Erling Følner, On groups with full Banach mean value, Math. Scand. 3 (1955), 243-254 Zbl0067.01203MR79220
  4. Y. Glasner, N. Monod, Amenable actions, free products and a fixed point property, Bull. Lond. Math. Soc. 39 (2007), 138-150 Zbl1207.43002MR2303529
  5. R. Grigorchuk, V. Nekrashevych, Amenable actions of nonamenable groups, Journal of Mathematical Sciences 140 (2007), 391-397 Zbl1127.43001MR2183217
  6. S. Moon, Amenable actions of amalgamated free products, Groups, Geometry and Dynamics 4 (2010), 309-332 Zbl1193.43001MR2595094

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