On relative property (T) and Haagerup's property

Authors:
Ionut Chifan and Adrian Ioana

Journal:
Trans. Amer. Math. Soc. **363** (2011), 6407-6420

MSC (2010):
Primary 20F69; Secondary 46L10

Published electronically:
July 14, 2011

MathSciNet review:
2833560

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Abstract: We consider the following three properties for countable discrete groups : (1) has an infinite subgroup with relative property (T), (2) the group von Neumann algebra has a diffuse von Neumann subalgebra with relative property (T) and (3) does not have Haagerup's property. It is clear that (1) (2) (3). We prove that both of the converses are false.

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Additional Information

**Ionut Chifan**

Affiliation:
Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nash- ville, Tennessee 37240 – and – Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Email:
ionut.chifan@vanderbilt.edu

**Adrian Ioana**

Affiliation:
Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-155505 – and – Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Email:
adiioana@math.ucla.edu

DOI:
https://doi.org/10.1090/S0002-9947-2011-05259-1

Received by editor(s):
July 14, 2009

Received by editor(s) in revised form:
November 23, 2009

Published electronically:
July 14, 2011

Additional Notes:
The second author was supported by a Clay Research Fellowship

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.