Stable actions of central extensions and relative property (T)
Group Theory
2017-05-23 v2 Dynamical Systems
Operator Algebras
Abstract
Let us say that a discrete countable group is stable if it has an ergodic, free, probability-measure-preserving and stable action. Let G be a discrete countable group with a central subgroup C. We present a sufficient condition and a necessary condition for G to be stable. We show that if the pair (G, C) does not have property (T), then G is stable. We also show that if the pair (G, C) has property (T) and G is stable, then the quotient group G/C is stable.
Keywords
Cite
@article{arxiv.1309.3739,
title = {Stable actions of central extensions and relative property (T)},
author = {Yoshikata Kida},
journal= {arXiv preprint arXiv:1309.3739},
year = {2017}
}
Comments
22 pages, 3 figures, minor corrections