A group upper central sequence
of the group terminates with
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. Referenced on
Wolfram|Alpha Nilpotent Group
Cite this as:
Renze, John . "Nilpotent Group." From MathWorld Eric
W. Weisstein . https://mathworld.wolfram.com/NilpotentGroup.html
Subject classifications
is nilpotent if the upper central sequence
for some 
.
