​Itay Kaplan: Dp-minimal omega-categorical groups are nilpotent-by-finite

Set Theory and Topology seminar (BGU)

​​Time: Tuesday, March 2nd, 12:30-13:45.

Place: Seminar room -101, Math building 58.
Speaker: ​Itay Kaplan (HUJI).

Title: Dp-minimal omega-categorical groups are nilpotent-by-finite (joint work with Elad Levi and Pierre Simon)

Abstract: Macpherson proved that omega-stable omega-categorical groups are nilpotent-by-finite. Krupinski and Krupinski with Dobrowolski (in two separate works, one with NIP, the other without) replaced the stability assumption by the much weaker assumption of being generically-stable.
We go to the other direction, and try to generalize Krupinski’s first result (NIP omega-categorical groups with fsg are nilpotent-by-finite) to remove the fsg assumption.
We succeed in the simplest NIP case, i.e., when the group is dp-minimal.

I will try to give a full proof of this result.
All concepts will be defined during the talk, but some basic knowledge of model theory (e.g., omega categorical theories) might be helpful.

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