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1
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Small profinite m-stable groups

100%
Wagner F.
Fundamenta Mathematicae
|
2003
|
tom 176
|
nr 2
181-191
EN
A small profinite m-stable group has an open abelian subgroup of finite ℳ-rank and finite exponent.
2
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Rigidity, internality and analysability

63%
Palacín D., Wagner F.
Fundamenta Mathematicae
|
2014
|
tom 224
|
nr 1
53-65
EN
We prove a version of Hrushovski's Socle Lemma for rigid groups in an arbitrary simple theory.
3
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On variants of CM-triviality

51%
Blossier T., Martin-Pizarro A., Wagner F.
Fundamenta Mathematicae
|
2012
|
tom 219
|
nr 3
253-262
EN
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.
4
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Around Podewski's conjecture

51%
Krupiński K., Tanović P., Wagner F.
Fundamenta Mathematicae
|
2013
|
tom 222
|
nr 2
175-193
EN
A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of almost linear minimal groups as certain valued groups.
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