Small cancellations over relatively hyperbolic groups and embedding theorems

Original · EN

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≥ 2. In particular, we give the affirmative answer to the well--known question of the existence of a finitely generated group G other than Z/2Z such that all nontrivial elements of G are conjugate.