arXiv 1111.05772011-11math.GR

Definable sets in a hyperbolic group

Olga Kharlampovich, Alexei Myasnikov

备注：: Corollary of Theorem 3 was corrected and incorporated into Theorem 3
发表信息：: International Journal of Algebra and Computation, 23, 1, 2013, pages 91:110

英文摘要：

We give a description of definable sets $P=(p_1,..., p_m)$ 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. This answers Malcev's question for $F$. As a corollary we show that proper non-cyclic subgroups of $F$ and $G$ are not definable and prove Bestvina and Feighn's result that definable subsets $P=(p)$ in a free group are either negligible or co-negligible in their terminology.

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