We conjecture that a finitely generated group has a decidable domino problem if and only if it is virtually free. We show this is true for all virtually nilpotent finitely generated groups (or, equivalently, groups of polynomial growth), and for all finitely generated groups whose center has a non-trivial, finitely generated and torsion-free subgroup.
Classification :
37-XX, 03-XX, 20-XX
Mots-clés :
Domino problem, groups of polynomial growth, virtually free groups, decidability, thick ends
Affiliations des auteurs :
Alexis Ballier
1
;
Maya Stein
1
1
Universidad de Chile, Santiago, Chile
Alexis Ballier; Maya Stein. The domino problem on groups of polynomial growth. Groups, geometry, and dynamics, Tome 12 (2018) no. 1, pp. 93-105. doi: 10.4171/ggd/439
@article{10_4171_ggd_439,
author = {Alexis Ballier and Maya Stein},
title = {The domino problem on groups of polynomial growth},
journal = {Groups, geometry, and dynamics},
pages = {93--105},
year = {2018},
volume = {12},
number = {1},
doi = {10.4171/ggd/439},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/439/}
}
TY - JOUR
AU - Alexis Ballier
AU - Maya Stein
TI - The domino problem on groups of polynomial growth
JO - Groups, geometry, and dynamics
PY - 2018
SP - 93
EP - 105
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/439/
DO - 10.4171/ggd/439
ID - 10_4171_ggd_439
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%J Groups, geometry, and dynamics
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%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/439/
%R 10.4171/ggd/439
%F 10_4171_ggd_439
