Abstract
We extend some basic properties of hyperbolic isometries of \({\mathbb{R}}\)-trees to the case of automorphisms of median pretrees.
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Adeleke, S.A., Neumann, P.M.: Relations related to betweenness: their structure and automorphisms. In: Memoirs of the American Mathematical Society, vol. 623. AMS, Providence (1998)
Bowditch, B.H.: Treelike structures arising from continua and convergence groups. In: Memoirs of the American Mathematical Society, vol. 662. AMS, Providence (1999)
Bowditch B.H., Crisp J.: Archimedean actions on median pretrees. Math. Proc. Camb. Phil. Soc. 130, 383–400 (2001)
Chiswell, I.M.: Protrees and Λ-trees. In: Kropholler, P.H. (ed.) Geometry and cohomology in group theory. London Mathematical Society Lecture Notes, vol. 252, pp. 74–87. Cambridge University Press, London (1995)
Culler M., Morgan J.W.: Group actions on \({\mathbb{R}}\)-trees. Proc. London. Math. Soc. (3) 55(3), 571–604 (1987)
Dress A.: Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces. Adv. Math. 53, 321–402 (1984)
Dunwoody M.J.: Groups acting on protrees. J. Lond. Math. Soc. (2) 56(1), 125–136 (1997)
Ivanov A.: Group actions on pretrees and definability. Comm. Algebra 32, 561–577 (2004)
Levitt G.: Non-nesting actions on real trees. Bull. Lond. Math. Soc. 30, 46–54 (1998)
Rosendal C.: A topological version of the Bergman property. Forum Math. 21, 299–332 (2009)
Serre J.: Trees. Springer, NY (1980)
Tits, J.: A “theorem of Lie-Kolchin” for trees, In: Bass, H., Cassidy, P.J., Kovacic, J. (eds.) Contributon to Algebra: A Collection of Papers Dedicated to Ellis Kolchin, pp. 377–388. Academic Press, NY (1977)
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The research is supported by KBN grant 2 P03A 007 19.
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Ivanov, A. Products of loxodromic automorphisms of pretrees. Beitr Algebra Geom 53, 105–112 (2012). https://doi.org/10.1007/s13366-011-0067-1
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DOI: https://doi.org/10.1007/s13366-011-0067-1