A nilpotent group is a group 
for which the group
upper central series
of the group terminates with 
for some 
.
Nilpotent groups have the property that each proper subgroup is properly contained in its normalizer.
A finite nilpotent group is the group direct product
of its Sylow p-subgroups.
See also
Group Center,
Group
Upper Central Series,
Nilpotent Lie Group
This entry contributed by John Renze
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References
Curtis, C. and Reiner, I. Methods of Representation Theory. New York: Wiley, 1981.Referenced on
Wolfram|Alpha
Nilpotent Group
Cite this as:
Weisstein, Eric W., with contributions by John Renze. "Nilpotent Group." From MathWorld--A
Wolfram Resource. https://mathworld.wolfram.com/NilpotentGroup.html
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