Small stable groups and generics

Journal of Symbolic Logic 56 (3):1026-1037 (1991)
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Abstract

We define an R-group to be a stable group with the property that a generic element (for any definable transitive group action) can only be algebraic over a generic. We then derive some corollaries for R-groups and fields, and prove a decomposition theorem and a field theorem. As a nonsuperstable example, we prove that small stable groups are R-groups

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Citations of this work

The model theory of unitriangular groups.Oleg V. Belegradek - 1994 - Annals of Pure and Applied Logic 68 (3):225-261.
Small skew fields.Cédric Milliet - 2007 - Mathematical Logic Quarterly 53 (1):86-90.
Another stable group.Andreas Baudisch - 1996 - Annals of Pure and Applied Logic 80 (2):109-138.

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