Journal of Symbolic Logic 65 (2):767-776 (2000)

Abstract
An $\omega$-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl-definable subgroup. Every finitely based regular type in a CM-trivial $\omega$-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple $\omega$-categorical CM-trivial theory has finite SU-rank.
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DOI http://projecteuclid.org/euclid.jsl/1183746076
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