On the structure of stable groups

Annals of Pure and Applied Logic 89 (1):85-92 (1997)

Abstract
In this paper, we shall survey results about the group-theoretic properties of stable groups. These can be classified into three main categories, according to the strength of the assumptions needed: chain conditions, generic types, and some form of rank. Each category has its typical application: Chain conditions often allow us to deduce global properties from local ones, generic properties are used to get definable groups from undefinable ones, and rank is necessary to interpret fields in certain group actions. While originally the main input came from algebraic group theory, founded on the similarities between rank and dimension, increasingly methods borrowed from finite group theory have come to play a rôle, emphasizing the study of characteristic subgroups and characteristic families of subgroups
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DOI 10.1016/s0168-0072(97)00004-3
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References found in this work BETA

A New Strongly Minimal Set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Superstable Groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.
Unidimensional Theories Are Superstable.Ehud Hrushovski - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.
Stability of Nilpotent Groups of Class 2 and Prime Exponent.Alan H. Mekler - 1981 - Journal of Symbolic Logic 46 (4):781-788.
Minimale Gruppen.Joachim Reineke - 1975 - Mathematical Logic Quarterly 21 (1):357-359.

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