Definable Envelopes of Nilpotent Subgroups of Groups with Chain Conditions on Centralizers

Tuna Altınel (1, 2, 3) , Paul Baginski (2)

1 AGL - Algèbre, géométrie, logique
2 ICJ - Institut Camille Jordan
3 UCBL - Université Claude Bernard Lyon 1

An $\mathfrak{M}_C$ group is a group in which all chains of centralizers have finite length. In this article, we show that every nilpotent subgroup of an $\mathfrak{M}_C$ group is contained in a definable subgroup which is nilpotent of the same nilpotence class. Definitions are uniform when the lengths of chains are bounded.

Mots clés: group theory; nilpotence; chains of centralizers; model theory; definability

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

Tuna Altınel, Paul Baginski. Definable Envelopes of Nilpotent Subgroups of Groups with Chain Conditions on Centralizers. Proceedings of the American Mathematical Society, 2014, 142 (5), pp.1497-1506. ⟨10.1090/S0002-9939-2014-11879-X⟩. ⟨hal-00703451⟩