Definable envelopes of nilpotent subgroups of groups with chain conditions on centralizers

Altınel, Tuna; Baginski, Paul

doi:10.1090/S0002-9939-2014-11879-X

Definable envelopes of nilpotent subgroups of groups with chain conditions on centralizers
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by Tuna Altınel and Paul Baginski PDF

Proc. Amer. Math. Soc. 142 (2014), 1497-1506 Request permission

Abstract:

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.

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