Dp-minimal omega-categorical groups are nilpotent-by-finite

par Itay Kaplan (Hebrew University)

mardi 12 avr. 2016, 14:30 → 15:30 Europe/Paris

112 (ICJ, salle 112, 1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua)

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.