English

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.

Keywords

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

R2 v1 2026-07-22T17:25:34.830Z