2012/12/11 by Oleg N. Ageev, Ageev, Oleg N.
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Mathematical Dynamics and Fractals #math.DS #math.GR #math.LO
paper · pdf · doi:10.48550/arxiv.1212.2660
30 pages
arxiv created 2012/12/11 · openalex publication_date 2012/12/11 · arxiv updated 2012/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For every countable abelian group G we find the set of all its subgroups H (H≤ G) such that a typical measure-preserving H-action on a standard atomless probability space (X,F, μ) can be extended to a free measure-preserving G-action on (X,F, μ). The description of all such pairs H≤ G was made in purely group terms, in the language of the dual G, and G-actions with discrete spectrum. As an application, we answer a question when a typical H-action can be extended to a G-action with some dynamic property, or to a G-action at all. In particular, we offer first examples of pairs H≤ G satisfying both G is countable abelian, and a typical H-action is not embeddable in a G-action.