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Fields interpretable in superrosy groups with NIP (the non-solvable case)
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- Journal:
- The Journal of Symbolic Logic / Volume 75 / Issue 1 / March 2010
- Published online by Cambridge University Press:
- 12 March 2014, pp. 372-386
- Print publication:
- March 2010
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- Article
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Let 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 < U b(G) < ∞. We prove that if G acts definably on a definable set of U р-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 U р-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 U р(G) = U р(H) + 1 and G/⋂g∈G Hg is not solvable-by-finite, then an infinite field interpretable in also exists.
of a rosy theory satisfying NIP. Assume that 