Infinite groups with large balls of torsion elements and small entropy
Group Theory
2010-08-04 v1
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.
Cite
@article{arxiv.math/0510141,
title = {Infinite groups with large balls of torsion elements and small entropy},
author = {Laurent Bartholdi and Yves de Cornulier},
journal= {arXiv preprint arXiv:math/0510141},
year = {2010}
}
Comments
8 pages; to appear in Archiv der Mathematik