Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T05:09:20.450Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on superstable groups

Published online by Cambridge University Press:  12 March 2014

Jerry Gagelman
Jerry Gagelman*
Affiliation:
Technische Universität Berlin, Institut für Mathematik, 3-3, Strasse des 17. Juni 136, 10623 Berlin, Germany, E-mail: gagelman@math.tu-berlin.de
Get accessRights & Permissions [Opens in a new window]

Abstract

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.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005, pp. 661 - 663
Copyright
Copyright © Association for Symbolic Logic 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1] Buechler, Steven, The geometry of weakly minimal types, this Journal, vol. 50 (1985), pp. 1044–1053.Google Scholar
[2] Gagelman, Jerry, Stability in geometric theories, Ph.D. thesis, University of Illinois at Urbana-Champaign, 05 2004.Google Scholar
[3] Hrushovski, Ehud and Pillay, Anand, Weakly normal groups, Logic Colloquium '85 (Paris Logic Group, editor), North-Holland, Amsterdam, 1987, pp. 233–44.CrossRefGoogle Scholar
[4] Lascar, Daniel, Omega-stable groups, Model theory and algebraic geometry (Bouscaren, Elizabeth, editor), Lecture Notes in Mathematics, vol. 1696, Springer, Berlin, 1998.CrossRefGoogle Scholar
[5] peterzil, Ya'acov, Pillay, Anand, and Starchenko, Sergei, Simple algebraic and semialgebraic groups over real closed fields, Transactions of the American Mathematical Society, vol. 352 (2000), pp. 4421–4450.CrossRefGoogle Scholar
[6] Pillay, Anand, On groups and fields definable in o-minimal structures, Journal of Pure and Applied Algebra, vol. 53 (1988), pp. 239–255.CrossRefGoogle Scholar
[7] Pillay, Anand and Pong, Wai Yan, On Lascar rank and Morley rank of definable groups in differentially closed fields, this Journal, vol. 67 (2002), pp. 1189–1196.Google Scholar
[8] Poizat, Bruno, Sous-groupes définissables d'un groupe stable, this Journal, vol. 46 (1981), pp. 137–146.Google Scholar