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Abstract: We start an analysis of geometric properties of a structure relative to areduct. In particular, we look at definability of groups and fields in thiscontext. In the relatively one-based case, every definable group is isogenousto a subgroup of a product of groups definable in the reducts. In therelatively CM-trivial case, which contains certain Hrushovski amalgamationsthe fusion of two strongly minimal sets or the expansions of a field by apredicate, every definable group allows a homomorphism with virtually centralkernel into a product of groups definable in the reducts.

Author: Thomas Blossier ICJ, Amador Martin Pizarro ICJ, Frank Olaf Wagner ICJ


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