Abstract
AbstractLet G be a group definable in a monster model of a rosy theory satisfying NIP. Assume that G has hereditarily finitely satisfiable generics and 1 < Ub(G) < ∞. We prove that if G acts definably on a definable set of Uр-rank 1, then, under some general assumption about this action, there is an infinite field interpretable in . We conclude that if G is not solvable-by-finite and it acts faithfully and definably on a definable set of Uр-rank 1, then there is an infinite field interpretable in . As an immediate consequence, we get that if G has a definable subgroup H such that Uр(G) = Uр(H) + 1 and G/⋂g∈GHg is not solvable-by-finite, then an infinite field interpretable in also exists.
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