no. 2
Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property
[Actions moyennables de produits amalgamés de groupes libres sur un sous-groupe cyclique et propriétés génériques]
Moon, Soyoung1
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, Tome 18 (2011) no. 2, pp. 211-229.

On montre que les produits amalgamés de groupes libres sur un sous-groupe cyclique admettent des actions moyennables, fidèles et transitives sur un ensemble dénombrable infini. Ce travail généralise le résultat concernant de telles actions pour les produits amalgamés de groupes libres sur deux générateurs.

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.

DOI : 10.5802/ambp.296
Classification : 43A07, 20E06, 57M07
Keywords: Amenable actions, amalgamated free products, Baire’s property
Mot clés : Actions moyennables, produits amalgamés, propriété de Baire
Moon, Soyoung 1

1 Institut de Mathématiques Université de Bourgogne UMR 5584 du CNRS 9 avenue Alain Savary - BP 47870 21078 Dijon cedex France 
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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, Tome 18 (2011) no. 2, pp. 211-229. doi : 10.5802/ambp.296. http://www.numdam.org/articles/10.5802/ambp.296/

[1] van Douwen, Eric K. Measures invariant under actions of F 2 , Topology Appl., Volume 34 (1990) no. 1, pp. 53-68 | DOI | MR | Zbl

[2] Fine, B.; Rosenberger, G. Algebraic generalizations of discret groups, Marcel Dekker, Inc., 1999 | MR | Zbl

[3] Følner, Erling On groups with full Banach mean value, Math. Scand., Volume 3 (1955), pp. 243-254 | MR | Zbl

[4] Glasner, Y.; Monod, N. Amenable actions, free products and a fixed point property, Bull. Lond. Math. Soc., Volume 39 (2007) no. 1, pp. 138-150 | DOI | MR | Zbl

[5] Grigorchuk, R.; Nekrashevych, V. Amenable actions of nonamenable groups, Journal of Mathematical Sciences, Volume 140 (2007) no. 3, pp. 391-397 | DOI | MR | Zbl

[6] Moon, S. Amenable actions of amalgamated free products, Groups, Geometry and Dynamics, Volume 4 (2010), pp. 309-332 | DOI | MR | Zbl

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