中文

Small cancellations over relatively hyperbolic groups and embedding theorems

群论 2011-07-12 v3

摘要

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.

关键词

引用

@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}
}

备注

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