Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published December 2019 | 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
Files (451.6 kB)
Name Size Download all
md5:f6b77b0cfdfaec1fceeae43890ca56f2
451.6 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023