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arXiv · math/0510141

Infinite groups with large balls of torsion elements and small entropy

Laurent Bartholdi·Yves de Cornulier
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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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Laurent Bartholdi, Yves de Cornulier. 2005-10-07. Infinite groups with large balls of torsion elements and small entropy. https://doi.org/10.1007/s00013-005-1684-4

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