The Journal of Symbolic Logic

Research Article

Supersimple ω-categorical groups and theories

David M. Evansa1 and Frank O. Wagnera2 c1

a1 School of Mathematics, UEA, Norwich NR4 7TJ, UK, E-mail:

a2 Mathematical Institute, University of Oxford, 24–29 ST Giles' Oxford Ox1 3LB., UK


An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl(ø)-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank.

(Received July 10 1998)

(Revised December 10 1998)

Key words and phrases

  • ω-categorical;
  • supersimple;
  • finite rank;
  • group;
  • abelian;
  • CM-trivial


c1 Current address: Institut Girard Desargues, Université Claude Bernard, Mathématiques, bâtiment, 101, 43, boulevard du 11 novembre 1918, 69622 Villeurbanne-cedex, France, E-mail:, E-mail: