Finiteness Properties and Profinite Completions
Abstract
In this note we show that various (geometric/homological) finiteness properties are not profinite properties. For example for every $1 \le k, \ell \le \bbn$, there exist two finitely generated residually finite groups $\Ga_1$ and $\Ga_2$ with isomorphic profinite completions, such that $\Ga_1$ is strictly of type $F_k$ and $\Ga_2$ of type $F_\ell$.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2012
- DOI:
- 10.48550/arXiv.1211.6573
- arXiv:
- arXiv:1211.6573
- Bibcode:
- 2012arXiv1211.6573L
- Keywords:
-
- Mathematics - Group Theory