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A note on a theorem of Chiswell


Authors: Stephen Jackson and Luca Q. Zamboni
Journal: Proc. Amer. Math. Soc. 123 (1995), 2629-2631
MSC: Primary 20E08
DOI: https://doi.org/10.1090/S0002-9939-1995-1277116-1
MathSciNet review: 1277116
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Abstract: In this note we give an alternative proof of a theorem of I. M. Chiswell which states that every finitely generated group which acts non-trivially on a $ \Lambda - $ tree admits a non-trivial action on an $ \mathbb{R} - $ tree.


References [Enhancements On Off] (What's this?)

  • [1] R. Alperin and H. Bass, Length functions of group actions on $ \Lambda - $ trees, Combinatorial Group Theory and Topology, Ann. of Math. Stud., no. 3, Princeton Univ. Press, Princeton, NJ, 1987, pp. 265-378. MR 895622 (89c:20057)
  • [2] I. M. Chiswell, Non-trivial group actions on $ \Lambda - $ trees, Bull. London Math. Soc. 24 (1992), 277-280. MR 1157264 (93d:20053)
  • [3] H. Enderton, A mathematical introduction to logic, Academic Press, New York, 1972. MR 0337470 (49:2239)
  • [4] P. B. Shalen, Dendrology of groups: an introduction, Essays in Group Theory (S. M. Gersten, ed.), Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 265-319. MR 919830 (89d:57012)

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DOI: https://doi.org/10.1090/S0002-9939-1995-1277116-1
Article copyright: © Copyright 1995 American Mathematical Society

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