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Groups acting on cubes and Kazhdan's property (T)
Author(s):
Graham
A.
Niblo;
Martin
A.
Roller
Journal:
Proc. Amer. Math. Soc.
126
(1998),
693-699.
MSC (1991):
Primary 20E34;
Secondary 20F32, 05C25
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Abstract:
We show that a group  contains a subgroup  with  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  with such a subgroup does not satisfy Kazhdan's property (T).
References:
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- P. de la Harpe, A. Valette, La propriété (T) de Kazhdan pour les groupes localement compacts, Asterisque 175 (1989). MR 90m:22001
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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