Let G be a group definable in a monster model 𝔠 of a rosy theory satisfying NIP. Assume that G has hereditarily finitely satisfiable generics and 1 < Uþ(G) < ∞. We prove that if G acts definably on a definable set of Uþ-rank 1, then, under some general assumption about this action, there is an infinite field interpretable in 𝔠. We conclude that if G is not solvable-by-finite and it acts faithfully and definably on a definable set of Uþ-rank 1, then there is an infinite field interpretable in 𝔠. As an immediate consequence, we get that if G has a definable subgroup H such that Uþ(G)=Uþ(H)+1 and G/⋂g ∈ GHg is not solvable-by-finite, then an infinite field interpretable in 𝔠 also exists.
"Fields interpretable in superrosy groups with NIP (the non-solvable case)." J. Symbolic Logic 75 (1) 372 - 386, March 2010. https://doi.org/10.2178/jsl/1264433927