Groups with finitely many conjugacy classes and their automorphisms
Groups with finitely many conjugacy classes and their automorphisms
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.
259-296
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
2009
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Minasyan, Ashot
(2009)
Groups with finitely many conjugacy classes and their automorphisms.
Commentarii Mathematici Helvetici, 84 (2), .
(doi:10.4171/CMH/162).
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.
Text
fin_classes-10.pdf
- Author's Original
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Submitted date: 1 April 2007
Published date: 2009
Organisations:
Pure Mathematics
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Local EPrints ID: 54841
URI: http://eprints.soton.ac.uk/id/eprint/54841
ISSN: 0010-2571
PURE UUID: ce1632a1-5e37-4d61-8b4b-b4fa7bdf0a8b
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Date deposited: 24 Oct 2008
Last modified: 16 Mar 2024 03:56
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