Titlebook: Arboreal Group Theory; Proceedings of a Wor Roger C. Alperin Conference proceedings 1991 Springer-Verlag New York, Inc. 1991 Group theory.a

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,?-Tree Actions are Not Determined by the Translation Lengths of Finitely Many Elements, Hom(.(2, ?)) is determined up to conjugation in .(2,?) by the traces of a finite set of elements of .. (See, for example, [.].) The purpose of this paper is to show that the analogue of this basic fact is not true for translation length functions of actions on ?-trees.

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0940-4740 rbolic geometry. Topics include the theory of length functions, structure of groups acting freely on trees, spaces of hyperbolic structures and their compactifications, and moduli for tree actions.978-1-4612-7811-5978-1-4612-3142-4Series ISSN 0940-4740

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Evaluating Business and Industry Trainingcial tree, the branching occurs at a discrete set of points, namely, the vertices, whereas in an ?-tree, there is no restriction on where branching may occur. The notion of ?-tree arose indirectly in the work of Lyndon [.]and Chiswell [.]concerning Lyndon length functions. The first definition was given by Tits in [.].

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