Definable Envelopes of Nilpotent Subgroups of Groups with Chain   Conditions on Centralizers
  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. 
Tuna Alt{\i}nel and Paul Baginski
math.LO