On ω-categorical groups and rings with NIP
نویسنده
چکیده
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 existence of a non-algebraic, generically stable over ∅ type, such a group is abelian.
منابع مشابه
Generically 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.
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