On variants of CM-triviality
Volume 219 / 2012
Fundamenta Mathematicae 219 (2012), 253-262 MSC: Primary 03C45. DOI: 10.4064/fm219-3-4
We introduce a generalisation 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 generalises 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.