Infinite Groups with Large Balls of Torsion Elements and Small Entropy

@inproceedings{Bartholdi2006InfiniteGW,
  title={Infinite Groups with Large Balls of Torsion Elements and Small Entropy},
  author={Laurent Bartholdi and Yves Cornulier},
  year={2006}
}
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. The Burnside Problem asks whether a finitely generated group all of whose elements have… CONTINUE READING