Published December 2019
| Version Submitted
Journal Article
Open
Strong amenability and the infinite conjugacy class property
Abstract
A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.
Additional Information
© 2019 Springer-Verlag GmbH Germany, part of Springer Nature. Received: 16 March 2018; Accepted: 7 June 2019; Published online: 13 July 2019. This work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz), and by NSF Grant DMS-1464475. We would like to thank Benjamin Weiss and Andrew Zucker for correcting mistakes in earlier drafts of this paper, and to likewise thank an anonymous referee for many corrections and suggestions. We would also like to thank Yair Hartman and Mehrdad Kalantar for drawing our attention to the relation of our results to the unique trace property of group von Neumann algebras.Attached Files
Submitted - 1801.04024.pdf
Files
1801.04024.pdf
Additional details
Identifiers
- Eprint ID
- 99832
- Resolver ID
- CaltechAUTHORS:20191114-102021413
Related works
- Describes
- https://arxiv.org/abs/1801.04024 (URL)
Funding
- Simons Foundation
- 419427
- NSF
- DMS-1464475
Dates
- Created
-
2019-11-14Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
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- Mathematics Department