Groups with finitely many conjugacy classes and their automorphisms
Abstract
We combine classical methods of combinatorial group theory with the theory of small cancellations over relatively hyperbolic groups to construct finitely generated torsionfree groups that have only finitely many classes of conjugate elements. Moreover, we present several results concerning embeddings into such groups. 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2007
 arXiv:
 arXiv:0704.0091
 Bibcode:
 2007arXiv0704.0091M
 Keywords:

 Mathematics  Group Theory;
 20F65;
 20E45;
 20F28
 EPrint:
 30 pages, 2 figures. Version 2: corrected several misprints and added new Lemma 6.4