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

Mathematics – Logic

Scientific paper

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Scientific paper

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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