Superrosy dependent groups having finitely satisfiable generics
Logic
2007-06-05 v1 Group Theory
Abstract
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.
Cite
@article{arxiv.0706.0486,
title = {Superrosy dependent groups having finitely satisfiable generics},
author = {Clifton Ealy and Krzysztof Krupinski and Anand Pillay},
journal= {arXiv preprint arXiv:0706.0486},
year = {2007}
}