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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-4,
author = {Thomas Blossier and Amador Martin-Pizarro and Frank O. Wagner},
title = {On variants of CM-triviality},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {253-262},
zbl = {1271.03052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-4}
}
Thomas Blossier; Amador Martin-Pizarro; Frank O. Wagner. On variants of CM-triviality. Fundamenta Mathematicae, Tome 219 (2012) pp. 253-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm219-3-4/