Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-13T15:37:07.767Z Has data issue: false hasContentIssue false
  • English
  • Français

Some examples of groups with no non-trivial action on a Λ-tree

Part of:Permutation groups

Published online by Cambridge University Press:  26 February 2010

I. M. Chiswell
I. M. Chiswell
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London El 4NS.
Get access

Extract

In [7] S. Pride gave a family of examples of finitely presented groups of cohomological dimension 2 having no non-trivial action on a simplicial tree. We show here that his examples have no non-trivial action on a Λ-tree, for any ordered abelian group Λ. This provides further slight evidence for an affirmative answer to Question A in §3.1 of [8]. We also give another similar family of examples.

MSC classification

Secondary:20B27: Infinite automorphism groups

Information

Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995, pp. 214 - 219
Copyright
Copyright © University College London 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Alperin, R. C. and Bass, H.. Length functions of group actions on Λ-trees. In Combinatorial group theory and topology (ed. Gersten, S. M. and Stallings, J. R.), Annals of Mathematics Studies 111, pp 265–378 (Princeton: University Press, 1987).CrossRefGoogle Scholar
2. Chiswell, I. M.. Non-trivial group actions on Λ-trees. Bull. London Math. Soc. 24 (1992), 277–280.CrossRefGoogle Scholar
3. Chiswell, I. M.. Harrison's theorem for Λ-trees. Quart. J. Math. Oxford (2), 45 (1994), 1–12.CrossRefGoogle Scholar
4. Gersten, S. M. and Short, H.. Small cancellation theory and automatic groups. Invent. Math., 102 (1990), 305–334.CrossRefGoogle Scholar
5. Gromov, M.. Hyperbolic groups. In Essays in group theory (ed. Gersten, S. M.), MSRI Publications 8, pp 75–263 (New York: Springer-Verlag, 1987).CrossRefGoogle Scholar
6. Paulin, F.. Outer automorphisms of hyperbolic groups and small actions on -trees. In Arboreal group theory (ed. Alperin, R. C.), MSRI Publications 19, pp 333–343 (New York: Springer-Verlag, 1991).Google Scholar
7. Pride, S. J.. Some finitely presented groups of cohomological dimension two with property (FA). J. Pure Appl. Algebra, 29 (1983), 167–168.CrossRefGoogle Scholar
8. Shalen, P. B.. Dendrology of groups: an introduction. In Essays in group theory (ed. Gersten, S. M.), MSRI Publications 8, pp 265–319 (New York: Springer-Verlag, 1987).CrossRefGoogle Scholar