Nilpotent Group

A group G is nilpotent if the upper central sequence


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.

See also

Group Center, Group Upper Central Series, Nilpotent Lie Group

This entry contributed by John Renze

Explore with Wolfram|Alpha


Curtis, C. and Reiner, I. Methods of Representation Theory. New York: Wiley, 1981.

Referenced on Wolfram|Alpha

Nilpotent Group

Cite this as:

Renze, John. "Nilpotent Group." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications