Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-20T06:15:45.464Z Has data issue: false hasContentIssue false
  • English
  • Français

On free actions on Λ-trees

Published online by Cambridge University Press:  24 October 2008

Mariusz Urbański  and
Luca Zamboni
Mariusz Urbański
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5116, U.S.A.
Luca Zamboni
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5116, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we show that if a group generated by two elements acts freely and without phantom inversions on a Λ-tree, then it is either free or free abelian.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 3 , May 1993 , pp. 535 - 542
Copyright
Copyright © Cambridge Philosophical Society 1993

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.)

References

REFERENCES

[1]Alperin, R. and Bass, H.. Length functions of group actions on Λ-trees. In Combinatorial Group Theory and Topology, Ann. of Math. Studies vol. 3 (Princeton University Press, 1987), pp. 265–378.Google Scholar
[2]Culler, M. and Morgan, J. W.. Groups actions on ℝ-trees. Proc. London Math. Soc. (3) 55 (1987), 571–604.CrossRefGoogle Scholar
[3]Davenport, H.. The Higher Arithmetic, 5th ed. (Cambridge University Press, 1982).Google Scholar
[4]Fine, B., Rohl, F. and Rosenberger, G.. Two-generator subgroups of certain HNN groups. In Combinatorial Group Theory, Contemporary Math. vol. 109 (American Mathematical Society, 1990), pp. 19–23.Google Scholar
[5]Harrison, N.. Real length functions in groups. Trans. Amer. Math. Soc. 174 (1972), 77–106.Google Scholar
[6]Morgan, J. W. and Shalen, P.. Valuations, trees and degenerations of hyperbolic structures I. Ann. of Math. 120 (1984), 401–176.Google Scholar
[7]Shalen, P.. Dendrology of groups. In Essays in Group Theory, Mathematical Sciences Research Institute Publications vol. 8 (Springer-Verlag, 1987), pp. 265–319.Google Scholar