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, Soyoung
Annales mathématiques Blaise Pascal, Tome 18 (2011), p. 211-229 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

Publié le : 2011-01-01
DOI : https://doi.org/10.5802/ambp.296
Classification:  43A07,  20E06,  57M07
Mots clés: Actions moyennables, produits amalgamés, propriété de Baire 
@article{AMBP_2011__18_2_211_0,
     author = {Moon, Soyoung},
     title = {Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {18},
     year = {2011},
     pages = {211-229},
     doi = {10.5802/ambp.296},
     zbl = {1246.43002},
     mrnumber = {2896486},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AMBP_2011__18_2_211_0}
}

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) pp. 211-229. doi : 10.5802/ambp.296. http://gdmltest.u-ga.fr/item/AMBP_2011__18_2_211_0/

[1] Van Douwen, Eric K. Measures invariant under actions of F 2 , Topology Appl., Tome 34 (1990) no. 1, pp. 53-68 | Article | MR 1035460 | Zbl 0701.43001

[2] Fine, B.; Rosenberger, G. Algebraic generalizations of discret groups, Marcel Dekker, Inc. (1999) | MR 1712997 | Zbl 0933.20001

[3] Følner, Erling On groups with full Banach mean value, Math. Scand., Tome 3 (1955), pp. 243-254 | MR 79220 | Zbl 0067.01203

[4] Glasner, Y.; Monod, N. Amenable actions, free products and a fixed point property, Bull. Lond. Math. Soc., Tome 39 (2007) no. 1, pp. 138-150 | Article | MR 2303529 | Zbl 1207.43002

[5] Grigorchuk, R.; Nekrashevych, V. Amenable actions of nonamenable groups, Journal of Mathematical Sciences, Tome 140 (2007) no. 3, pp. 391-397 | Article | MR 2183217 | Zbl 1127.43001

[6] Moon, S. Amenable actions of amalgamated free products, Groups, Geometry and Dynamics, Tome 4 (2010), pp. 309-332 | Article | MR 2595094 | Zbl 1193.43001