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arxiv: math/0411039 · v3 · pith:PCZDXV5Qnew · submitted 2004-11-02 · 🧮 math.GR

Small cancellations over relatively hyperbolic groups and embedding theorems

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keywords groupshyperbolicfinitelygeneratedmathbbrelativelysmallaffirmative
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We generalize the small cancellation theory over hyperbolic groups developed by Olshanskii to the case of relatively hyperbolic groups. This allows us to construct infinite finitely generated groups with exactly $n$ conjugacy classes for every $n\ge 2$. In particular, we give the affirmative answer to the well--known question of the existence of a finitely generated group $G$ other than $\mathbb Z/2\mathbb Z$ such that all nontrivial elements of $G$ are conjugate.

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