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On variants of CM-triviality
Thomas Blossier 1   ; Amador Martin-Pizarro 2   ; Frank O. Wagner 2
1 Université de Lyon, CNRS, Université Lyon 1 Institut Camille Jordan, UMR 5208 43 boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex, France
2 Université de Lyon, CNRS Université Lyon 1, Institut Camille Jordan, UMR 5208 43 boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex, France
Fundamenta Mathematicae, Tome 219 (2012) no. 3, pp. 253-262 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm219-3-4
Keywords: introduce generalisation cm triviality relative fixed invariant collection partial types analogy canonical base property defined pillay ziegler chatzidakis which generalises one basedness under condition stable field internal family group finite lascar rank has normal nilpotent subgroup quotient almost internal family

Thomas Blossier  1   ; Amador Martin-Pizarro  2   ; Frank O. Wagner  2

1 Université de Lyon, CNRS, Université Lyon 1 Institut Camille Jordan, UMR 5208 43 boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex, France
2 Université de Lyon, CNRS Université Lyon 1, Institut Camille Jordan, UMR 5208 43 boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex, France 
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Thomas Blossier; Amador Martin-Pizarro; Frank O. Wagner. On variants of CM-triviality. Fundamenta Mathematicae, Tome 219 (2012) no. 3, pp. 253-262. doi: 10.4064/fm219-3-4

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