Groups acting on cubes and Kazhdan’s property (T)
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- by Graham A. Niblo and Martin A. Roller PDF
- Proc. Amer. Math. Soc. 126 (1998), 693-699 Request permission
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).References
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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
- Received by editor(s): September 9, 1996
- Communicated by: Ronald M. Solomon
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 693-699
- MSC (1991): Primary 20E34; Secondary 20F32, 05C25
- DOI: https://doi.org/10.1090/S0002-9939-98-04463-3
- MathSciNet review: 1459140