English

Small cancellations over relatively hyperbolic groups and embedding theorems

Group Theory 2011-07-12 v3

Abstract

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 nn conjugacy classes for every n2n\ge 2. In particular, we give the affirmative answer to the well--known question of the existence of a finitely generated group GG other than Z/2Z\mathbb Z/2\mathbb Z such that all nontrivial elements of GG are conjugate.

Keywords

Cite

@article{arxiv.math/0411039,
  title  = {Small cancellations over relatively hyperbolic groups and embedding theorems},
  author = {D. V. Osin},
  journal= {arXiv preprint arXiv:math/0411039},
  year   = {2011}
}

Comments

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