Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Reference15 articles.
1. [5] Guralnick, R. and Malle, G. , Products of conjugacy classes and fixed point spaces, preprint, arXiv:1005.3756.
2. Ultraproducts and Chevalley groups;Point;Archive for Mathematical Logic,1999
3. Rings with a polynomial identity;Kaplansky;Bulletin of the American Mathematical Society,1948
4. Measurable groups of low dimension;Elwes;Mathematical Logic Quarterly,2008
5. Simple Theories
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