Jackson, Stephen; Zamboni, Luca Q. A note on a theorem of Chiswell. (English) Zbl 0841.20029 Proc. Am. Math. Soc. 123, No. 9, 2629-2631 (1995). Summary: 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. Cited in 1 Document MSC: 20E08 Groups acting on trees 20F65 Geometric group theory 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces 20F05 Generators, relations, and presentations of groups Keywords:action on \(\mathbb{R}\)-tree; finitely generated group; \(\Lambda\)-tree PDFBibTeX XMLCite \textit{S. Jackson} and \textit{L. Q. Zamboni}, Proc. Am. Math. Soc. 123, No. 9, 2629--2631 (1995; Zbl 0841.20029) Full Text: DOI References: [1] Roger Alperin and Hyman Bass, Length functions of group actions on \Lambda -trees, Combinatorial group theory and topology (Alta, Utah, 1984) Ann. of Math. Stud., vol. 111, Princeton Univ. Press, Princeton, NJ, 1987, pp. 265 – 378. · Zbl 0978.20500 [2] I. M. Chiswell, Nontrivial group actions on \Lambda -trees, Bull. London Math. Soc. 24 (1992), no. 3, 277 – 280. · Zbl 0791.20022 · doi:10.1112/blms/24.3.277 [3] Herbert B. Enderton, A mathematical introduction to logic, Academic Press, New York-London, 1972. · Zbl 0298.02002 [4] Peter B. Shalen, Dendrology of groups: an introduction, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 265 – 319. · Zbl 0649.20033 · doi:10.1007/978-1-4613-9586-7_4 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.