xpyq = zr and groups that act freely on Λ-trees">
Journal article

The equation xpyq = zr and groups that act freely on Λ-trees

  • Brady, N. Department of Mathematics, University of Oklahoma, Norman, USA
  • Ciobanu, Laura Department of Mathematics, University of Fribourg, Switzerland
  • Martino, A. Department of Mathematics, Universitat Politecnica de Catalunya, Castelldefels, Spain
  • Rourke, S. O. Department of Mathematics, Cork Institute of Technology, Ireland
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    2009
Published in:
  • Transactions of the American Mathematical Society. - 2009, vol. 361, no. 1, p. 223-236
English 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 xpy q = zr with integers p, q, r 4, then x , y and z commute. As a result, the one-relator groups with xpy q = zr as relator, are examples of hyperbolic and CAT( 1) groups which do not act freely on any Λ-tree.
Faculty
Faculté des sciences et de médecine
Department
Département de Mathématiques
Language
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/300874
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