  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.
