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

Abstract
We define an $\mathfrak{R}$-group to be a stable group with the property that a generic element can only be algebraic over a generic. We then derive some corollaries for $\mathfrak{R}$-groups and fields, and prove a decomposition theorem and a field theorem. As a nonsuperstable example, we prove that small stable groups are $\mathfrak{R}$-groups.
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DOI 10.2307/2275070
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References found in this work BETA

Superstable Groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.
Superstable Fields and Groups.G. Cherlin - 1980 - Annals of Mathematical Logic 18 (3):227.
Semisimple Stable and Superstable Groups.J. T. Baldwin & A. Pillay - 1989 - Annals of Pure and Applied Logic 45 (2):105-127.

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Citations of this work BETA

The Model Theory of Unitriangular Groups.Oleg V. Belegradek - 1994 - Annals of Pure and Applied Logic 68 (3):225-261.
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Nilpotent Complements and Carter Subgroups in Stable ℜ-Groups.Frank O. Wagner - 1994 - Archive for Mathematical Logic 33 (1):23-34.
Another Stable Group.Andreas Baudisch - 1996 - Annals of Pure and Applied Logic 80 (2):109-138.

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