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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Received: 3 August 2005
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Bartholdi, L., de Cornulier, Y. Infinite groups with large balls of torsion elements and small entropy. Arch. Math. 87, 104–112 (2006). https://doi.org/10.1007/s00013-005-1684-4
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DOI: https://doi.org/10.1007/s00013-005-1684-4