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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.

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Correspondence to Yoshikata Kida.

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Kida, Y. Stable actions of central extensions and relative property (T). Isr. J. Math. 207, 925–959 (2015). https://doi.org/10.1007/s11856-015-1167-7

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Keywords

  • Unitary Representation
  • Discrete Group
  • Central Extension
  • Measurable Subset
  • Neutral Element