External definability and groups in NIP theories
نویسندگان
چکیده
منابع مشابه
External definability and groups in NIP theories
We prove that many properties and invariants of definable groups in NIP theories, such as definable amenability, G/G00, etc., are preserved when passing to the theory of the Shelah expansion by externally definable sets, Mext, of a model M . In the light of these results we continue the study of the “definable topological dynamics” of groups in NIP theories. In particular we prove the Ellis gro...
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We show that any pseudofinite group with NIP theory and with a finite upper bound on the length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite group is soluble-by-finite. This generalises, and shortens the proof of, an earlier result for stable pseudofinite groups. An example is given of an NIP pseudofinite group which is not soluble-by-finite. However,...
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Let M be an arbitrary structure. We say that an M -formula φ(x) defines a stable set in M if every formula φ(x)∧α(x, y) is stable. We prove: If G is an M -definable group and every definable stable subset of G has U-rank at most n (the same n for all sets) then G has a maximal connected stable normal subgroup H such that G/H is purely unstable. The assumptions holds for example when the structu...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2014
ISSN: 0024-6107
DOI: 10.1112/jlms/jdu019