Skip to main content Accessibility help

Supersimple ω-categorical groups and theories

  • David M. Evans (a1) and Frank O. Wagner (a2)

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.

Corresponding author
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:
Hide All
[1]Baur, Walter, Cherlin, Gregory, and Macintyre, Angus, Totally categorical groups and rings, Journal of Algebra, vol. 57 (1979), pp. 407440.
[2]Bergman, George M. and Lenstra, Hendrik W. Jr., Subgroups close to normal subgroups, Journal of Algebra, vol. 127 (1989), pp. 8097.
[3]Cherlin, Gregory, Harrington, Leo, and Lachlan, Alistair, 0-categoricalℵ0-stable structures, Annals of Pure and Applied Logic, vol. 28 (1985), pp. 103135.
[4]Hart, Bradd, Kim, Byunghan, and Pillay, Anand, Coordinatization and canonical bases in simple theories, to appear in this Journal.
[5]Hrushovski, Ehud, Smoothly approximated structures, unpublished notes, 1991.
[6]Hrushovski, Ehud, A new strongly minimal set, Annals of Pure and Applied Logic, vol. 62 (1993), pp. 147166.
[7]Hrushovski, Ehud, Simplicity and the Lascar group, notes, 1997.
[8]Kim, Byunghan, A note on Lascar strong types in simple theories, this Journal, vol. 63 (1998), pp. 926936.
[9]Kim, Byunghan and Pillay, Anand, From stability to simplicity, The Bulletin of Symbolic Logic, vol. 4 (1998), pp. 1736.
[10]Macpherson, H. D., Absolutely ubiquitous structures and ℵ0-categorical groups, Quarterly Journal of Mathematics, Oxford, vol. 39 (1988), pp. 483500.
[11]Pillay, Anand, The geometry of forking and groups of finite Morley rank, this Journal, vol. 60 (1995), pp. 12511259.
[12]Poizat, Bruno, Groupes stables, Nur al mantiq wal marifah, 1988.
[13]Pourmahdian, Massoud, notes, 1998.
[14]Schlichting, G., Operationen mit periodischen Stabilisatoren, Archiv der Mathematik (Basel), vol. 34 (1980), pp. 9799.
[15]Wagner, Frank O., Groups in simple theories, submitted to this Journal, 1997.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed