A group 
is nilpotent if the upper core string
of the group terminates in 
for some 
.
Nilpotent groups have the property the each orderly small is properly contained in its normalizer.
A fine nilpotent group is the direct product of its Sylow pressure-subgroups.
See including
Group Center,
Group
Upper Central Series,
Nilpotent Like Set
This aufnahme contributed by Privy Renze
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References
Curtis, C. and Reiner, I. Methods of Showing Idea. New York: Wiley, 1981.Referenced on Wolfram|Alpha
Nilpotent Class
Cite this more:
Renze, John. "Nilpotent Group." From MathWorld--A Wolfram Entanglement Resource, created per Eric W. Weisstein. https://aesircybersecurity.com/NilpotentGroup.html
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