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Infinite groups with large balls of torsion elements and small entropy

Authors
  • Bartholdi, Laurent1
  • de Cornulier, Yves2
  • 1 Institut de Mathématiques B (IMB), École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland , Lausanne (Switzerland)
  • 2 Université de Neuchâtel, Institut de Mathématiques, Rue Émile Argand 11, Neuchâtel, CH-2007, Switzerland , Neuchâtel (Switzerland)
Type
Published Article
Journal
Archiv der Mathematik
Publisher
Birkhäuser-Verlag
Publication Date
Aug 01, 2006
Volume
87
Issue
2
Pages
104–112
Identifiers
DOI: 10.1007/s00013-005-1684-4
Source
Springer Nature
Keywords
License
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Abstract

We exhibit infinite, solvable, virtually abelian groups with a fixed number of generators, having arbitrarily large balls consisting of torsion elements. We also provide a sequence of 3-generator non-virtually nilpotent polycyclic groups of algebraic entropy tending to zero. All these examples are obtained by taking appropriate quotients of finitely presented groups mapping onto the first Grigorchuk group.

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