Effective embedding of residually hyperbolic groups into direct products of extensions of centralizers

Details Effective embedding of residually hyperbolic groups into direct products of extensions of centralizers Effective embedding of residually hyperbolic groups into direct products of extensions of centralizers

2012-02-17

arxiv.org/abs/1202.3835v1

Mathematics

Group Theory

28 pages

Scientific paper

For any torsion-free hyperbolic group $\Gamma$ and any group $G$ that is fully residually $\Gamma$, we construct algorithmically a finite collection of homomorphisms from $G$ to groups obtained from $\Gamma$ by extensions of centralizers, at least one of which is injective. When $G$ is residually $\Gamma$, this gives a effective embedding of $G$ into a direct product of such groups. We also give an algorithmic construction of a diagram encoding the set of homomorphisms from a given finitely presented group to $\Gamma$.

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