Definable subsets in a hyperbolic group

Details Definable subsets in a hyperbolic group Definable subsets in a hyperbolic group

2011-11-02

arxiv.org/abs/1111.0577v2

Mathematics

Group Theory

Scientific paper

We give a description of definable subsets in a free non-abelian group $F$ and in a torsion-free non-elementary hyperbolic group $G$ that follows from our work on the Tarski problems. As a corollary we show that proper non-cyclic subgroups of $F$ and $G$ are not definable (this answers Malcev's question for $F$) and prove Bestvina and Feighn's result that definable subsets in a free group are either negligible or co-negligible.

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