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Journal Articles The Journal of Symbolic Logic Year : 2020

Dimensional groups and fields

Frank Olaf Wagner
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We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. 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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Dates and versions

hal-01235178 , version 1 (28-11-2015)
hal-01235178 , version 2 (17-09-2018)
hal-01235178 , version 3 (26-08-2019)


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Frank Olaf Wagner. Dimensional groups and fields. The Journal of Symbolic Logic, 2020, 85 (3), pp.918-936. ⟨10.1017/jsl.2020.48⟩. ⟨hal-01235178v3⟩
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