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16.70 (2006)

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Suppose that a finitely generated group $G$ acts freely on an $\Lambda$-tree, where $\Lambda$ is an ordered abelian group. Is it true that $G$ acts freely on a $\mathbb{Z}^n$-tree for some $n$?

Contributor: A. G. Myasnikov, V. N. Remeslennikov, O. G. Kharlampovich

Progress

Comment of 2013: It was proved that every finitely presented group acting freely on an $\Lambda$-tree acts freely on some $\mathbb{R}^n$-tree for a suitable $n$, where $\mathbb{R}$ has the lexicographical order (O. Kharlampovich, A. Myasnikov, D. Serbin, Int. J. Algebra Comput., 23 (2013), 325–345).

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