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Subsimple groups

Published online by Cambridge University Press:  12 March 2014

Frank Wagner
Frank Wagner*
Affiliation:
Institut Girard Desargues, Université Claude Bernard (LYON-1), Mathématiques, Bâtiment 101, 21 Avenue Claude Bernard, 69622 Villeurbanne-Cedex, France, E-mail: wagner@math.univ-lyonl.fr
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Abstract

We define a notion of genericity for arbitrary subgroups of groups interpretable in a simple theory, and show that a type generic for such a group is generic for the minimal hyperdefinable supergroup (the definable hull). In particular, at least one generic type of the definable hull is finitely satisfiable in the original subgroup. If the subgroup is a subfield. then the additive and the multiplicative definable hull both have bounded index in the smallest hyperdefinable superfield.

Keywords

simplicitysubgroupgenericsimple field
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 4 , December 2005 , pp. 1365 - 1370
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

[1]Wagner, F. O., Subgroups of stable groups, this Journal, vol. 55 (1990), pp. 151–156.Google Scholar
[2]Wagner, F. O., Simple theories, Kluwer Academic Publishers, Dordrecht, 2000.CrossRefGoogle Scholar
[3]Wagner, F. O., Fields of finite Morley rank, this Journal, vol. 66 (2001), pp. 703–706.Google Scholar