Definable envelopes in groups with simple theory

Cédric Milliet (1, 2)

1 ICJ - Institut Camille Jordan
2 Département de Mathématiques

Let G be a group with simple theory. For any nilpotent subgroup N of class n, there is a definable nilpotent group E of class at most 2.n finitely many translates of which cover N. The group E is definable with parameters in N. If S is a soluble subgroup of G of derived length l, there is a definable soluble group F of derived length at most 2.l finitely many translates of which cover S. The group F is definable with parameters in S.

Mots clés: group with simple theory; nilpotent group; soluble group; definable envelope; FC-nilpotent group; FC-soluble group

Domaines: Logique [math.LO]

Cédric Milliet. Definable envelopes in groups with simple theory. 2012. ⟨hal-00657716v1⟩