THE EQUATION xy = z AND GROUPS THAT ACT FREELY ON Λ-TREES
نویسنده
چکیده
Let G be a group that acts freely on a Λ-tree, where Λ is an ordered abelian group, and let x, y, z be elements in G. We show that if xpyq = zr with integers p, q, r ≥ 4, then x, y and z commute. As a result, the one-relator groups with xpyq = zr as relator, are examples of hyperbolic and CAT(−1) groups which do not act freely on any Λ-tree.
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تاریخ انتشار 2008