March 15
Chris Natoli,
CUNY
Omega-categorical, dp-minimal groups are nilpotent-by-finite
I will present results by Kaplan, Levi, and Simon (2017) showing that groups with two model-theoretic properties – omega-categorical and dp-minimal – are nilpotent-by-finite, i.e., they have normal nilpotent subgroups of finite index. Nilpotent-by-finite is a strong group-theoretic property, which can inform the use of groups in exploring various theories, including the theories of structures other than groups. This talk will define these properties (nilpotent-by-finite, omega-categorical, dp-minimal, as well as NIP), give examples of structures with and without these properties, and explain the group-theoretic consequences of the model-theoretic properties that are used in the paper.