Small cancellations over relatively hyperbolic groups and embedding theorems

Details Small cancellations over relatively hyperbolic groups and embedding theorems Small cancellations over relatively hyperbolic groups and embedding theorems

2004-11-02

arxiv.org/abs/math/0411039v3

Mathematics

Group Theory

Final version, appendix is added. Published in Annals of Math. 172 (2010), 1-39

Scientific paper

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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