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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The full group of a countable measurable equivalence relation


Author: Richard Mercer
Journal: Proc. Amer. Math. Soc. 117 (1993), 323-333
MSC: Primary 28D99; Secondary 28D05
MathSciNet review: 1139480
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1139480-1
PII: S 0002-9939(1993)1139480-1
Article copyright: © Copyright 1993 American Mathematical Society