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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Groups acting on cubes
and Kazhdan's property (T)


Authors: Graham A. Niblo and Martin A. Roller
Journal: Proc. Amer. Math. Soc. 126 (1998), 693-699
MSC (1991): Primary 20E34; Secondary 20F32, 05C25
MathSciNet review: 1459140
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Abstract: We show that a group $G$ contains a subgroup $K$ with $e(G,K) > 1$ if and only if it admits an action on a connected cube that is transitive on the hyperplanes and has no fixed point. As a corollary we deduce that a countable group $G$ with such a subgroup does not satisfy Kazhdan's property (T).


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Additional Information

Graham A. Niblo
Affiliation: Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
Email: gan@maths.soton.ac.uk

Martin A. Roller
Affiliation: Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Email: Martin.Roller@mathematik.uni-regensburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04463-3
PII: S 0002-9939(98)04463-3
Keywords: Geometric group theory, ends, Kazhdan's property (T)
Received by editor(s): September 9, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society