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Published November 2000 | Published
Journal Article Open

Coding Subset Shift by Subgroup Conjugacy

Gao, Su

Abstract

We present a Borel reduction from a subset shift equivalence relation of a countable group to a subgroup conjugacy relation of a free product. The technique gives a much shorter proof of an earlier result of Thomas and Velickovic.

Additional Information

© 2000 London Mathematical Society. Received 23 June 1999; revised 16 November 1999. I thank G. Hjorth, A. S. Kechris and S. Thomas for very helpful discussions on this subject, and the referee for suggestions to improve an earlier version of this paper. Finally, I should point out a very recent result of A. Andretta, R. Camerlo and G. Hjorth which states that if G is a countable group containing a nonabelian free subgroup, then Ec(G) is a universal countable Borel equivalence relation.

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