Stable actions of central extensions and relative property (T)

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.

22 pages, 3 figures, minor corrections

References in corpus (3)

• Inner amenability for groups and central sequences in factors
• Stability in orbit equivalence for Baumslag-Solitar groups and Vaes groups
• Inner amenable groups having no stable action

Cited by in corpus (5)

• Invariant means and the structure of inner amenable groups
• Inner amenable groupoids and central sequences
• Stable actions and central extensions
• Splitting in orbit equivalence, treeable groups, and the Haagerup property
• Groups with infinite FC-center have the Schmidt property