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Article
The Full Group of a Countable Measurable Equivalence Relation
Proceedings of the American Mathematical Society
  • Richard Mercer, Wright State University - Main Campus
Document Type
Article
Publication Date
2-1-1993
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.

Comments

First published in Proceedings of the American Mathematical Society 117.2 (1993), published by the American Mathematical Society.

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/