CM-Triviality and stable groups

Journal of Symbolic Logic 63 (4):1473-1495 (1998)
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Abstract

We define a generalized version of CM-triviality, and show that in the presence of enough regular types, or solubility, a stable CM-trivial group is nilpotent-by-finite. A torsion-free small CM-trivial stable group is abelian and connected. The first result makes use of a generalized version of the analysis of bad groups

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10.2307/2586662

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Citations of this work

Mekler's construction preserves CM-triviality.Andreas Baudisch - 2002 - Annals of Pure and Applied Logic 115 (1-3):115-173.
CM-triviality and relational structures.Viktor Verbovskiy & Ikuo Yoneda - 2003 - Annals of Pure and Applied Logic 122 (1-3):175-194.

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References found in this work

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.
More on ${\germ R}$.Frank O. Wagner - 1992 - Notre Dame Journal of Formal Logic 33 (2):159-174.
On stable torsion-free nilpotent groups.Claus Grünenwald & Frieder Haug - 1993 - Archive for Mathematical Logic 32 (6):451-462.
Stable groups, mostly of finite exponent.Frank O. Wagner - 1993 - Notre Dame Journal of Formal Logic 34 (2):183-192.

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