Submission date: 3 December 2012.

Abstract:

We classify the groups definable in the coloured fields obtained by Hrushovski amalgamation. A group definable in the bad green field is isogenous to the quotient of a subgroup of an algebraic group by a Cartesian power of the group of green elements. A definable subgroup of an algebraic group in the green or red field is an extension of a Cartesian power of the subgroup of coloured elements by an algebraic group. In particular, a simple group in a coloured field is algebraic.

Mathematics Subject Classification:

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Full text arXiv 1211.7235: pdf, ps.