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 tree admits a non-trivial action on an tree.

**[1]**R. Alperin and H. Bass,*Length functions of group actions on**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**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