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On free actions on Λ-trees

Published online by Cambridge University Press:  24 October 2008

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.

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
Copyright
Copyright © Cambridge Philosophical Society 1993

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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. 265378.Google Scholar
[2]Culler, M. and Morgan, J. W.. Groups actions on ℝ-trees. Proc. London Math. Soc. (3) 55 (1987), 571604.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. 1923.Google Scholar
[5]Harrison, N.. Real length functions in groups. Trans. Amer. Math. Soc. 174 (1972), 77106.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. 265319.Google Scholar