Hostname: page-component-6bf8c574d5-5ws7s Total loading time: 0 Render date: 2025-03-09T14:22:14.981Z Has data issue: false hasContentIssue false
  • English
  • Français

GROUPS OF MORLEY RANK 4

Published online by Cambridge University Press:  22 January 2016

JOSHUA WISCONS
JOSHUA WISCONS*
Affiliation:
DEPARTMENT OF MATHEMATICSHAMILTON COLLEGECLINTON, NY 13323, USAE-mail: jwiscons@hamilton.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that any simple group of Morley rank 4 must be a bad group with no proper definable subgroups of rank larger than 1. We also give an application to groups acting on sets of Morley rank 2.

Keywords

Primary 03C60Secondary 20B22finite Morley ranksimple groupgeneric transitivity
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 1 , March 2016 , pp. 65 - 79
Copyright
Copyright © The Association for Symbolic Logic 2016 

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.)

References

REFERENCES

Altınel, Tuna, Borovik, Alexandre V., and Cherlin, Gregory, Simple groups of finite Morley rank, Mathematical Surveys and Monographs, vol. 145, American Mathematical Society, Providence, RI, 2008.Google Scholar
Altınel, Tuna and Burdges, Jeffrey, On analogies between algebraic groups and groups of finite Morley rank. Journal of the London Mathematical Society (2), vol. 78 (2008), no. 1, pp. 213–232.CrossRefGoogle Scholar
Borovik, Alexandre, Burdges, Jeffrey, and Cherlin, Gregory, Involutions in groups of finite Morley rank of degenerate type. Selecta Mathematica, vol. 13 (2007), no. 1, pp. 1–22.Google Scholar
Borovik, Alexandre and Cherlin, Gregory, Permutation groups of finite Morley rank, Model theory with applications to algebra and analysis, Vol. 2, London Mathematical Society Lecture Note Series, vol. 350, Cambridge University Press, Cambridge, 2008, pp. 59–124.Google Scholar
Borovik, Alexandre and Nesin, Ali, Groups of finite Morley rank, Oxford Logic Guides, vol. 26, The Clarendon Press, Oxford University Press, New York, 1994, Oxford Science Publications.CrossRefGoogle Scholar
Burdges, Jeffrey and Cherlin, Gregory, Semisimple torsion in groups of finite Morley rank. Journal of Mathematical Logic, vol. 9 (2009), no. 2, pp. 183–200.Google Scholar
Cherlin, Gregory, Groups of small Morley rank. Annals of Mathematical Logic, vol. 17 (1979), no. 1–2, pp. 1–28.Google Scholar
Deloro, Adrien, Groupes simples connexes minimaux algébriques de type impair. Journal of Algebra, vol. 317 (2007), no. 2, pp. 877–923.CrossRefGoogle Scholar
Frécon, Olivier, Pseudo-tori and subtame groups of finite Morley rank. Journal of Group Theory, vol. 12 (2009), no. 2, pp. 305–315.CrossRefGoogle Scholar
Gropp, Ursula, There is no sharp transitivity on q 6when q is a type of Morley rank 2, this Journal, vol. 57 (1992), no. 4, pp. 1198–1212.Google Scholar
Poizat, Bruno, Groupes stables, Nur al-Mantiq wal-Ma'rifah [Light of Logic and Knowledge], 2, Bruno Poizat, Lyon, 1987, Une tentative de conciliation entre la géométrie algébrique et la logique mathématique. [An attempt at reconciling algebraic geometry and mathematical logic].Google Scholar