Abstract
Groups with length functions were introduced by Lyndon [5], and those with integer valued length were shown by Chiswell [2] to be equivalent to groups acting on trees, investigated by Serre[6]. Watatani[7] showed that for a group with integer valued length function the edges of the tree form an orthonormal set in a Hilbert space on which the group acts as a group of isometries.
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More From: Mathematical Proceedings of the Cambridge Philosophical Society
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