From “Metabelian ℚ-Vector Spaces” to New ω-Stable Groups

E-ISSN： 1943-5894|2|1|84-93

ISSN： 1079-8986

Source： Bulletin of Symbolic Logic, Vol.2, Iss.1, 1996-03, pp. : 84-93

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Abstract

The aim of this paper is to describe (without proofs) an analogue of the theory of nontrivial torsion-free divisible abelian groups for metabelian groups. We obtain illustrations for “old-fashioned” model theoretic algebra and “new” examples in the theory of stable groups. We begin this paper with general considerations about model theory. In the second section we present our results and we give the structure of the rest of the paper. Most parts of this paper use only basic concepts from model theory and group theory (see [14] and especially Chapters IV, V, VI and VIII for model theory, and see for example [23] and especially Chapters II and V for group theory). However, in Section 5, we need some somewhat elaborate notions from stability theory. One can find the beginnings of this theory in [14], and we refer the reader to [16] or [21] for stability theory and to [22] for stable groups.