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
See alsoGroup Center
Upper Central Series
, Nilpotent Lie Group
This entry contributed by John Renze
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ReferencesCurtis, C. and Reiner, I. Methods of Representation Theory. New York: Wiley, 1981.
Cite this as:
Renze, John. "Nilpotent Group." From MathWorld--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/NilpotentGroup.html