Skip to main content
Article thumbnail
Location of Repository

Groups with finitely many conjugacy classes and their automorphisms

By Ashot Minasyan


We combine classical methods of combinatorial group theory with the theory of small cancellation over relatively hyperbolic groups to construct finitely generated torsion-free groups that have only finitely many classes of conjugate elements. Moreover, we present several results concerning embeddings into such groups.<br/>As another application of these techniques, we prove that every countable group C can be realized as a group of outer automorphisms of a group N, where N is a finitely generated group having Kazhdan’s property (T) and containing exactly two conjugacy classes

Topics: QA
Year: 2009
OAI identifier:
Provided by: e-Prints Soton

Suggested articles


  1. (2001). All groups are outer automorphism groups of simple groups, doi
  2. (1989). Any group is represented by an outer automorphism group,
  3. (2005). Diagrams with selection and method for constructing boundedly generated and boundedly simple groups, doi
  4. (2006). Elementary subgroups of relatively hyperbolic groups and bounded generation, doi
  5. (1949). Embedding theorems for groups, doi
  6. (2005). Every group is an outer automorphism group of a finitely generated group, doi
  7. (2007). Finitely generated infinite simple groups of infinite commutator width, doi
  8. (2007). Finitely presentable, non-Hopfian groups with Kazhdan’s Property and infi-nite outer automorphism group, doi
  9. (1989). Geometry of defining relations in groups, doi
  10. (2007). Kazhdan groups with infinite outer automorphism group,
  11. (1989). La propri´ et´ e (T) de Kazhdan pour les groupes localement compacts, (avec un appendice de Marc Burger). Ast´ erisque 175,
  12. (1993). On residualing homomorphisms and G-subgroups of hyperbolic groups, doi
  13. (1991). Outer automorphisms of hyperbolic groups and small actions on R-trees, Arboreal Group Theory doi
  14. (2007). Peripheral fillings of relatively hyperbolic groups, doi
  15. (2006). Relative Dehn functions of HNN-extensions and amalgamated products, Topological and asymptotic aspects of group theory, doi
  16. (2006). Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, doi
  17. (2006). Rips construction and Kazhdan property (T), doi
  18. (1953). Simple Free Products, doi
  19. Small cancellations over relatively hyperbolic groups and embedding theorems, doi
  20. (2006). The Kourovka notebook. Unsolved problems in group theory, 16th augmented
  21. (2007). The SQ-universality and residual properties of relatively hyperbolic groups, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.