On Variants of CM-triviality

Thomas Blossier, Amador Martin-Pizarro, Frank Olaf Wagner

Published 2012-05-31, updated 2012-10-16Version 2

We introduce a generalization of CM-triviality relative to a fixed invariant collection of partial types, in analogy to the Canonical Base Property defined by Pillay, Ziegler and Chatzidakis which generalizes one-basedness. We show that, under this condition, a stable field is internal to the family, and a group of finite Lascar rank has a normal nilpotent subgroup such that the quotient is almost internal to the family.