, Volume 28, Issue 2, pp 267–271 | Cite as

Generating Sym(ω) by Permutations Preserving Dense Orders

  • Aleksander Ivanov


We show how generic permutations of ω can be presented by products of permutations preserving dense orders.


Permutations Dense orders 

Mathematics Subject Classifications (2010)

03C64 03E15 20E08 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adeleke, S.A., Neumann, P.M.: Relations related to betweenness: their structure and automorphisms. Mem. Am. Math. Soc. 131(623) (1998)Google Scholar
  2. 2.
    Bowditch, B.H.: Treelike structures arising from continua and convergence groups. Mem. Am. Math. Soc. 662 (1999)Google Scholar
  3. 3.
    Bowditch, B.H, Crisp, J.: Archimedean actions on median pretrees. Math. Proc. Cambridge Phil. Soc. 130, 383–400 (2001)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bestvina, M.: R-trees in topology, geometry, and group theory. In: Daverman, R.J., Sher, R.B. (eds.) Handbook of Geometric Topology, pp. 55–91. North-Holland, Amsterdam (2002)Google Scholar
  5. 5.
    Dunwoody, M.J.: Groups acting on protrees. J. Lond. Math. Soc. 56(2), 125–136 (1997)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Guirardel, V., Ivanov, A.: Non-nesting actions of Polish groups on real trees. J. Pure Appl. Algebra 214, 2074–2077 (2010)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Ivanov, A.: Group actions on pretrees and definability. Commun. Algebra 32, 561–577 (2004)MATHCrossRefGoogle Scholar
  8. 8.
    Kechris, A.: Classical Descriptive Set Theory. Springer (1995)Google Scholar
  9. 9.
    Macpherson, D.H., Thomas, S.: Comeagre conjugacy classes and free products with amalgamation. Discrete Math. 291, 135–142 (2005)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Rosendal, C: A topological version of the Bergman property. Forum Math. 21, 299–332 (2009)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Truss, J.K.: Generic automorphisms of homogeneous structures. Proc. Lond. Math. Soc. 65, 121–141 (1992)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WrocławWrocławPoland

Personalised recommendations