A Fitting Theorem for Simple Theories

Daniel Palacin (1) , Frank Olaf Wagner (2, 3)

1 Institut für Mathematische Logik und Grundlagenforschung
2 ICJ - Institut Camille Jordan
3 AGL - Algèbre, géométrie, logique

The Fitting subgroup of a type-definable group in a simple theory is relatively definable and nilpotent. Moreover, the Fitting subgroup of a supersimple hyperdefinable group has a normal hyperdefinable nilpotent subgroup of bounded index, and is itself of bounded index in a hyperdefinable subgroup.

Mots clés: simple theory; group; nilpotent; Fitting subgroup

Domaines: Logique [math.LO]; Théorie des groupes [math.GR]

Daniel Palacin, Frank Olaf Wagner. A Fitting Theorem for Simple Theories. Bulletin of the London Mathematical Society, 2016. ⟨hal-01073018v3⟩