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

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