## Journal of Symbolic Logic

### Small Stable Groups and Generics

Frank O. Wagner

#### Abstract

We define an $\mathfrak{R}$-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 $\mathfrak{R}$-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.

#### Article information

Source
J. Symbolic Logic, Volume 56, Issue 3 (1991), 1026-1037.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183743749

Digital Object Identifier
doi:10.2178/jsl/1183743749

Mathematical Reviews number (MathSciNet)
MR1129165

Zentralblatt MATH identifier
0743.03028

JSTOR