In mathematics, specifically group theory, a nilpotent group G is a group that has an upper central series that terminates with G. Equivalently, it has a central series of finite length or its lower central series terminates with {1}.

In mathematics, more specifically ring theory, an ideal I of a ring R is said to be a nilpotent ideal if there exists a natural number k such that Ik = 0.

In linear algebra, a nilpotent matrix is a square matrix N such that

Element squared equals zero eventually.

Algebra whose powers eventually vanish.