The triviality problem for profinite completions

Author: 

Bridson, M
Wilton, H

Publication Date: 

24 February 2015

Journal: 

Inventiones Mathematicae

Last Updated: 

2019-12-12T09:00:30.34+00:00

Issue: 

2

Volume: 

202

DOI: 

10.1007/s00222-015-0578-8

page: 

839-874

abstract: 

© 2015, Springer-Verlag Berlin Heidelberg. We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this property remains undecidable among the fundamental groups of compact, non-positively curved square complexes. We deduce that many other properties of groups are undecidable. For hyperbolic groups, there cannot exist algorithms to determine largeness, the existence of a linear representation with infinite image (over any infinite field), or the rank of the profinite completion.

Symplectic id: 

575129

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article