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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 \({\text {II}}_1\) 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.

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Correspondence to Yoshikata Kida.

Additional information

The author was supported by JSPS Grant-in-Aid for Scientific Research, No. 25800063.

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Kida, Y. Stable actions and central extensions. Math. Ann. 369, 705–722 (2017).

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