The full group of a countable measurable equivalence relation
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- by Richard Mercer PDF
- Proc. Amer. Math. Soc. 117 (1993), 323-333 Request permission
Abstract:
We study the group of all "$R$-automorphisms" of a countable equivalence relation $R$ on a standard Borel space, special Borel automorphisms whose graphs lie in $R$. We show that such a group always contains periodic maps of each order sufficient to generate $R$. A construction based on these periodic maps leads to totally nonperiodic $R$-automorphisms all of whose powers have disjoint graphs. The presence of a large number of periodic maps allows us to present a version of the Rohlin Lemma for $R$-automorphisms. Finally we show that this group always contains copies of free groups on any countable number of generators.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 323-333
- MSC: Primary 28D99; Secondary 28D05
- DOI: https://doi.org/10.1090/S0002-9939-1993-1139480-1
- MathSciNet review: 1139480