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Preprint Number 967
967. Frank Olaf Wagner
Dimensional groups and fields (Former title: Pseudofinite Mc-groups.)
Submission date: 30 November 2015. Revised 19 September 2018.
A pseudofinite group satisfying the uniform chain condition on centralizers up to finite index has a big finite-by-abelian subgroup.
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 pseudofinite groups contain big finite-by-abelian subgroups, and pseudofinite groups of dimension 2 contain big soluble subgroups.
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