The domino problem on groups of polynomial growth

Alexis Ballier, Maya Stein

Published 2013-11-17, updated 2014-11-24Version 2

We characterize the virtually nilpotent finitely generated groups (or, equivalently by Gromov's theorem, groups of polynomial growth) for which the Domino Problem is decidable: These are the virtually free groups, i.e. finite groups, and those having $\Z$ as a subgroup of finite index.