Document Type
Article
Publication Date
2-1993
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.
Repository Citation
Mercer, R.
(1993). The Full Group of a Countable Measurable Equivalence Relation. Proceedings of the American Mathematical Society, 117 (2), 323-333.
https://corescholar.libraries.wright.edu/math/4
DOI
10.2307/2159164
Comments
First published in Proceedings of the American Mathematical Society 117.2 (1993), published by the American Mathematical Society.