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In mathematics, especially in the fields of group theory and Lie theory, a central series is a kind of normal series of subgroups or Lie subalgebras, expressing the idea that the commutator is nearly trivial. For groups, this is an explicit expression that the group is a nilpotent group, and for matrix rings, this is an explicit expression that in some basis the matrix ring consists entirely of upper triangular matrices with constant diagonal.
This article uses the language of group theory; analogous terms are used for Lie algebras.
The lower central series and upper central series , are, despite the "central" in their names, central series if and only if a group is nilpotent.
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