Small stable groups and generics

Journal of Symbolic Logic 56 (3):1026-1037 (1991)
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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DOI 10.2178/jsl/1183743749
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Oleg V. Belegradek (1994). The Model Theory of Unitriangular Groups. Annals of Pure and Applied Logic 68 (3):225-261.
Andreas Baudisch (1996). Another Stable Group. Annals of Pure and Applied Logic 80 (2):109-138.

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