Nilpotency Class

For a nilpotent group, the nilpotency class (or nilpotent class) is the smallest positive integer c such that the (c+1)-st term of the lower central series is trivial, equivalently the least c for which all iterated commutators of length c+1 vanish.

For a nilpotent group or Lie algebra, the nilpotency class (or class of nilpotency) is the smallest integer c such that the (c+1)-th term of the lower central series is trivial; it quantifies how many nontrivial commutator steps are needed before reaching the trivial subgroup or zero algebra.