On $𝜔$-categorical groups and rings with NIP
نویسندگان
چکیده
منابع مشابه
On ω-categorical groups and rings with NIP
We show that ω-categorical rings with NIP are nilpotent-by-finite. We prove that an ω-categorical group with NIP and fsg is nilpotent-by-finite. We also notice that an ω-categorical group with at least one strongly regular type is abelian. Moreover, we get that each ω-categorical, characteristically simple p-group with NIP has an infinite, definable abelian subgroup. Assuming additionally the e...
متن کاملGenerically stable, ω-categorical groups and rings
In two recent papers with Krzysztof Krupi´nski, we proved that every ω-categorical, generically stable group is nilpotent-by-finite and that every ω-categorical, generically stable ring is nilpotent-by-finite. During the lecture, after a brief overview of well-known results on ω-categorical groups and rings, I will explain the main ideas of the proofs of our results.
متن کاملOn ω-categorical, generically stable groups and rings
We prove that every ω-categorical, generically stable group is nilpotent-byfinite and that every ω-categorical, generically stable ring is nilpotent-by-finite.
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We prove that each ω-categorical, generically stable group is solvable-byfinite.
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An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU -rank. Every definable subgroup is commensurable with an acl(∅)definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU -rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU -rank.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-11102-x