Superrosy dependent groups having finitely satisfiable generics

Ealy, Clifton; Krupinski, Krzysztof; Pillay, Anand

Superrosy dependent groups having finitely satisfiable generics

Authors

Ealy, Clifton

Krupinski, Krzysztof

Pillay, Anand

Description

We study a model theoretic context (finite thorn rank, NIP, with finitely satisfiable generics) which is a common generalization of groups of finite Morley rank and definably compact groups in o-minimal structures. We show that assuming thorn rank 1, the group is abelian-by-finite, and assuming thorn rank 2 the group is solvable by finite. Also a field is algebraically closed.