Journal of Symbolic Logic

A note on superstable groups

Jerry Gagelman

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


It is proved that all groups of finite U-rank that have the descending chain condition on definable subgroups are totally transcendental. A corollary is that any stable group that is definable in an o-minimal structure is totally transcendental of finite Morley rank.

Article information

J. Symbolic Logic, Volume 70, Issue 2 (2005), 661-663.

First available in Project Euclid: 1 July 2005

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Gagelman, Jerry. A note on superstable groups. J. Symbolic Logic 70 (2005), no. 2, 661--663. doi:10.2178/jsl/1120224734.

Export citation


  • Steven Buechler The geometry of weakly minimal types, Journal of Symbolic Logic, vol. 50 (1985), pp. 1044--1053.
  • Jerry Gagelman Stability in geometric theories, Ph.D. thesis, University of Illinois at Urbana-Champaign, May 2004.
  • Ehud Hrushovski and Anand Pillay Weakly normal groups, Logic Colloquium '85 (Paris Logic Group, editor), North-Holland, Amsterdam,1987, pp. 233--44.
  • Daniel Lascar Omega-stable groups, Model theory and algebraic geometry (Elizabeth Bouscaren, editor), Lecture Notes in Mathematics, vol. 1696, Springer, Berlin,1998.
  • Ya'acov Peterzil, Anand Pillay, and Sergei Starchenko Simple algebraic and semialgebraic groups over real closed fields, Transactions of the American Mathematical Society, vol. 352 (2000), pp. 4421--4450.
  • Anand Pillay On groups and fields definable in o-minimal structures, Journal of Pure and Applied Algebra, vol. 53 (1988), pp. 239--255.
  • Anand Pillay and Wai Yan Pong On Lascar rank and Morley rank of definable groups in differentially closed fields, Journal of Symbolic Logic, vol. 67 (2002), pp. 1189--1196.
  • Bruno Poizat Sous-groupes définissables d'un groupe stable, Journal of Symbolic Logic, vol. 46 (1981), pp. 137--146.