A group G is nilpotent if the upper central sequence 1 = Z_0<=Z_1<=Z_2<=...<=Z_n<=... of the group terminates with Z_n = G for some n. Nilpotent groups have the property that each proper subgroup is properly contained in its normalizer. A finite nilpotent group is the direct product of its Sylow p-subgroups.

group center | group upper central series | nilpotent Lie group