Groups with finitely many conjugacy classes and their automorphisms


Minasyan, Ashot (2009) Groups with finitely many conjugacy classes and their automorphisms Commentarii Mathematici Helvetici, 84, (2), pp. 259-296. (doi:10.4171/CMH/162).

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Description/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.
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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.4171/CMH/162
ISSNs: 0010-2571 (print)
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ePrint ID: 54841
Date :
Date Event
1 April 2007Submitted
2009Published
Date Deposited: 24 Oct 2008
Last Modified: 16 Apr 2017 17:45
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/54841

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