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Groups with finitely many conjugacy classes and their automorphisms

By Ashot Minasyan

Abstract

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: oai:eprints.soton.ac.uk:54841
Provided by: e-Prints Soton

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