Actions, length functions, and non-archemedian words

In this paper we survey recent developments in the theory of groups acting on $Λ$-trees. We are trying to unify all significant methods and techniques, both classical and recently developed, in an attempt to present various faces of the theory and to show how these methods can be used to solve major problems about finitely presented $Λ$-free groups. Besides surveying results known up to date we draw many new corollaries concerning structural and algorithmic properties of such groups.

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