On the Complexity of the Isomorphism Relation for
Finitely Generated Groups
Authors: Simon Thomas, and Boban Velickovic
ABSTRACT
Working within the framework of descriptive set theory,
we show that the isomorphism relation for finitely
generated groups is a universal essentially countable
Borel equivalence relation. We also prove the corresponding
result for the conjugacy relation for subgroups of the free
group on two generators. The proofs are group-theoretic,
and we refer to descriptive set theory only for the relevant
definitions and for motivation for the results.
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