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Article
The Full Group of a Countable Measurable Equivalence Relation
Proceedings of the American Mathematical Society
Document Type
Article
Publication Date
2-1-1993
Disciplines
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.
DOI
10.2307/2159164
Citation Information
Richard Mercer. "The Full Group of a Countable Measurable Equivalence Relation" Proceedings of the American Mathematical Society Vol. 117 Iss. 2 (1993) p. 323 - 333 ISSN: 0002-9939 Available at: http://works.bepress.com/richard_mercer/1/
First published in Proceedings of the American Mathematical Society 117.2 (1993), published by the American Mathematical Society.