Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T23:58:11.351Z Has data issue: false hasContentIssue false
  • English
  • Français

Bad groups of finite Morley rank

Published online by Cambridge University Press:  12 March 2014

Luis Jaime Corredor
Luis Jaime Corredor*
Affiliation:
Mathematisches Institut, Beringstrasse 4, D-5300 Bonn, West Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove the following theorem. Let G be a connected simple bad group (i.e. of finite Morley rank, nonsolvable and with all the Borel subgroups nilpotent) of minimal Morley rank. Then the Borel subgroups of G are conjugate to each other, and if B is a Borel subgroup of G, then , NG(B) = B, and G has no involutions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 3 , September 1989 , pp. 768 - 773
Copyright
Copyright © Association for Symbolic Logic 1989

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

[BCM]Baur, W., Cherlin, G., and Macintyre, A., Totally categorical groups and rings, Journal of Algebr, vol. 57 (1979), pp. 407–440.CrossRefGoogle Scholar
[BaS]Baldwin, J. and Saxl, J., Logical stability in group theory, Journal of the Australian Mathematical Society, Series A, vol. 21 (1976), pp. 267–276.CrossRefGoogle Scholar
[Ch]Cherlin, G., Groups of small Morley rank, Annals of Mathematical Logic, vol. 17 (1979), pp. 1–28.CrossRefGoogle Scholar
[Hu]Humphreys, J. E., Linear algebraic groups, Springer-Verlag, Berlin, 1975.CrossRefGoogle Scholar
[M]Morley, M., Categoricity in power, Transactions of the American Mathematical Society, vol. 114 (1965), pp. 514–538.CrossRefGoogle Scholar
[Ma1]Macintyre, A., On ω 1-categorical theories of abelian groups, Fundamenta Mathematicae, vol. 70(1971), pp. 253–270.CrossRefGoogle Scholar
[Ma2]Macintyre, A., On ω 1-categorical theories of fields, Fundamental Mathematicae, vol. 71 (1971), pp. 1–25.CrossRefGoogle Scholar
[N1]Nesin, A., Zil'ber's results, preprint.Google Scholar
[N2]Nesin, A., Non-solvable groups of Morley rank 3, preprint.Google Scholar
[P1]Poizat, B., Missionary mathematics, this Journal, vol. 53 (1988), pp. 132–145.Google Scholar
[P2]Poizat, B., Groupes stables, Nur al-Mantiq wal-Ma'rifah. Villeurbanne, 1987.Google Scholar
[P&B]Poizat, B. and Borovik, V., Mauvais groupes, Sibirskiĭ Mathematičeskiĭ Žurnal (to appear; Russian): English translation, Siberian Mathematical Journal (to appear).Google Scholar
[R]Robinson, D. J. S., A course in the theory of groups, Springer-Verlag, Berlin, 1982.CrossRefGoogle Scholar
[S]Serre, J. P., A course in arithmetic, Springer-Verlag, Berlin, 1985.Google Scholar
[Th]Thomas, S., Model theory of locally finite groups, I, preprint.Google Scholar
[Zi]Zil′ber, B. I., The structure of models of categorical theories and the non-finite-axiomatizability problem, preprint, Kemerovo, 1977 = Manuscript No. 2800-77, deposited at VINITI, 1977. (Russian)Google Scholar