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DIMENSIONAL GROUPS AND FIELDS

Part of: Special aspects of infinite or finite groups Model theory Connections with logic

Published online by Cambridge University Press:  05 October 2020

FRANK O. WAGNER
FRANK O. WAGNER*
Affiliation:
UNIVERSITÉ LYON 1, CNRS INSTITUT CAMILLE JORDAN UMR 5208 21 AVENUE CLAUDE BERNARD 69622VILLEURBANNE CEDEX, FRANCEE-mail: wagner@math.univ-lyon1.fr
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Abstract

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimension. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that a pseudofinite $\widetilde {\mathfrak M}_c$ -group of finite positive dimension contains a finite-by-abelian subgroup of positive dimension, and a pseudofinite group of dimension 2 contains a soluble subgroup of dimension 2.

Keywords

dimensionchain conditiongroupdomainskew fielddefinabilitypseudofinite group of small dimension

MSC classification

Primary: 03C45: Classification theory, stability and related concepts
Secondary: 03C20: Ultraproducts and related constructions 03C60: Model-theoretic algebra 12L12: Model theory 20F24: FC-groups and their generalizations
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 918 - 936
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Copyright
© The Association for Symbolic Logic 2020

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