Infinite groups with large balls of torsion elements and small entropy

Details Infinite groups with large balls of torsion elements and small entropy Infinite groups with large balls of torsion elements and small entropy

2005-10-07

arxiv.org/abs/math/0510141v1

Archiv der Mathematik 87(2), 104-112, 2006

Mathematics

Group Theory

8 pages; to appear in Archiv der Mathematik

Scientific paper

10.1007/s00013-005-1684-4

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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