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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
Full-text PDF Free Access
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Additional Information
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).
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- G.P. Scott, Ends of pairs of groups, Journal of Pure and Applied Algebra 11 (1977), 179-198. MR 81h:20047
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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
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