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Inversion is Possible in Groups with no Periodic Automorphisms

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  05 June 2015

Martin R. Bridson  and
Hamish Short
Martin R. Bridson
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Oxford OX2 6GG, UK (bridson@maths.ox.ac.uk)
Hamish Short
Affiliation:
Aix Marseille Université, Centre National de la Recherche Scientifique, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France (hamish@cmi.univ-mrs.fr)
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Abstract

There exist infinite finitely presented torsion-free groups G such that Aut(G) and Out(G) are torsion free but G has an automorphism sending some non-trivial element to its inverse.

Keywords

group automorphismshyperbolic groupscomplete groups

MSC classification

Secondary: 20E36: Automorphisms of infinite groups 20F67: Hyperbolic groups and nonpositively curved groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 11 - 16
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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