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The geometry of forking and groups of finite Morley rank

Published online by Cambridge University Press:  12 March 2014

Anand Pillay
Anand Pillay*
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, E-mail: anand.pillay.1@nd.edu
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Abstract

The notion of CM-triviality was introduced by Hrushovski, who showed that his new strongly minimal sets have this property. Recently Baudisch has shown that his new ω1-categorical group has this property. Here we show that any group of finite Morley rank definable in a CM-trivial theory is nilpotent-by-finite, or equivalently no simple group of finite Morley rank can be definable in a CM-trivial theory.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 4 , December 1995 , pp. 1251 - 1259
Copyright
Copyright © Association for Symbolic Logic 1995

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References

REFERENCES

[B1, 2]Baudisch, A., A new uncountably categorical group. I, II, Transactions of the American Mathematical Society (to appear).Google Scholar
[BP]Borovik, A. and Poizat, B., Simple groups of finite Morley rank without nonnilpotent connected subgroups, preprint. (Russian)Google Scholar
[Ch]Cherlin, G., Groups of small Morley rank, Annals of Mathematical Logic, vol. 17 (1979), pp. 1–28.CrossRefGoogle Scholar
[Co]Corredor, L. J., Bad groups of finite Morley rank, this Journal, vol. 54 (1989), pp. 768–773.Google Scholar
[H1]Hrushovski, E., Locally modular regular types, Classification theory: proceedings of the U.S.-Israel binational workshop on model theory in mathematical logic held in Chicago, Illinois, 1985 (Baldwin, J. T., editor), Lecture Notes in Mathematics, vol. 1292, Springer-Verlag, Berlin, 1987, pp. 132–164.CrossRefGoogle Scholar
[H2]Hrushovski, E., A new strongly minimal set, Annals of Pure and Applied Logic, vol. 62 (1993), pp. 147–166.CrossRefGoogle Scholar
[HP]Hrushovski, E. and Pillay, A., Weakly normal groups, Logic colloquium '85 (Berline, Ch.et al., editors), North-Holland, Amsterdam, 1987, pp. 233–244.CrossRefGoogle Scholar
[N]Nesin, A., Nonsolvable groups of Morley rank 3, Journal of Algebra, vol. 124 (1989), pp. 199–218.CrossRefGoogle Scholar
[P1]Pillay, A., Simple superstable theories, Classification theory: proceedings of the U.S.-lsrael binational workshop on model theory in mathematical logic held in Chicago, Illinois 1985 (Baldwin, J. T., editor), Lecture Notes in Mathematics, vol. 1292, Springer-Verlag, Berlin, 1987, pp. 247–263.CrossRefGoogle Scholar
[P2]Pillay, A., Geometrical stability theory, Oxford University Press, Oxford (to appear).Google Scholar
[Po]Poizat, B., Groupes stables, Nur al-Mantiq wal ma'Rifah, Villeurbanne, 1987.Google Scholar