Stable actions and central extensions
A probability measure preserving action of a countable group is called stable if its transformation groupoid absorbs the ergodic hyperfinite equivalence relation of type \text {II}}_1$$II1 under direct product. We show that for a countable group G and its central subgroup C, if G C has a stable action, then so does G. Combining a previous result of the author, we obtain a characterization of a central extension having a stable action.