A group
is nilpotent if the upper central sequence

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 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:
Renze, John . "Nilpotent Group." From MathWorld --A Wolfram Web Resource, created by Eric
W. Weisstein . https://mathworld.wolfram.com/NilpotentGroup.html

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