Geodesic
Highly transitive actions of free products
Moon, Soyoung1 ; Stalder, Yves2
1Institut de Mathématiques de Bourgogne, Université de Bourgogne, UMR 5584 du CNRS, BP 47870, 21078 Dijon, France
2Laboratoire de Mathématiques, Clermont Université, Université Blaise Pascal, BP 10448, 63000 Clermont-Ferrand, France
Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 589-607
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We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group PSL2(ℤ) ≃ (ℤ∕2ℤ) ∗ (ℤ∕3ℤ) admits a faithful and highly transitive action on a countable set.

DOI : 10.2140/agt.2013.13.589
Classification : 20B22, 20E06
Keywords: highly transitive actions, free products, Baire category Theorem

Moon, Soyoung  1   ; Stalder, Yves  2

1 Institut de Mathématiques de Bourgogne, Université de Bourgogne, UMR 5584 du CNRS, BP 47870, 21078 Dijon, France
2 Laboratoire de Mathématiques, Clermont Université, Université Blaise Pascal, BP 10448, 63000 Clermont-Ferrand, France 
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Moon, Soyoung; Stalder, Yves. Highly transitive actions of free products. Algebraic and Geometric Topology, Tome 13 (2013) no. 1, pp. 589-607. doi: 10.2140/agt.2013.13.589

[1] M Bestvina, R–trees in topology, geometry, and group theory, from: "Handbook of geometric topology" (editors R J Daverman, R B Sher), North-Holland (2002) 55

[2] J D Dixon, Most finitely generated permutation groups are free, Bull. London Math. Soc. 22 (1990) 222

[3] S Garion, Y Glasner, Highly transitive actions of Out(Fn), to appear in Groups, Geometry and Dynamics (2011)

[4] A M W Glass, S H Mccleary, Highly transitive representations of free groups and free products, Bull. Austral. Math. Soc. 43 (1991) 19

[5] S V Gunhouse, Highly transitive representations of free products on the natural numbers, Arch. Math. (Basel) 58 (1992) 435

[6] K K Hickin, Highly transitive Jordan representations of free products, J. London Math. Soc. (2) 46 (1992) 81

[7] D Kitroser, Highly-transitive actions of surface groups, Proc. Amer. Math. Soc. 140 (2012) 3365

[8] S Moon, Permanence properties of amenable, transitive and faithful actions, Bull. Belg. Math. Soc. Simon Stevin 18 (2011) 287

[9] B H Neumann, Groups covered by permutable subsets, J. London Math. Soc. 29 (1954) 236

[10] P M Neumann, The structure of finitary permutation groups, Arch. Math. (Basel) 27 (1976) 3

[11] J P Serre, Arbres, amalgames, SL2, 46, Société Mathématique de France (1977)

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