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Fields interpretable in superrosy groups with NIP (the non-solvable case)

Published online by Cambridge University Press:  12 March 2014

Krzysztof Krupiński
Krzysztof Krupiński*
Affiliation:
Instytut Matematyczny Uniwersytetu Wrocławskiego, Pl. Grunwaldzki 2/4 50-384 Wroclaw, Poland Mathematics Department, University of Illinois at Urbana -Champaign, 1409 W. Green Street, Urbana, IL 61801, USA, E-mail: [email protected]
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Abstract

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.

Keywords

superrosy groupinterpretable fieldnon independence property
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 1 , March 2010 , pp. 372 - 386
Copyright
Copyright © Association for Symbolic Logic 2010

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