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Omega-1 of center is normality-large in nilpotent p-group

407 bytes added, 13:46, 23 September 2008
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Note that if <math>G</math> is a finite p-group, i.e., a [[group of prime power order]], then it is nilpotent.
 
==Related facts==
 
===Corollaries===
 
* [[Minimal normal implies contained in Omega-1 of center for nilpotent p-group]]
* [[Socle equals Omega-1 of center for nilpotent p-group]]
* [[Minimal characteristic implies contained in Omega-1 of center for nilpotent p-group]]
 
===Other related facts===
 
* [[Minimal normal implies central in nilpotent]]
* [[Minimal characteristic implies central in nilpotent]]
==Facts used==
* # [[Nilpotent implies center is normality-large]]* # [[Omega-1 is large]] (and hence, is normality-large)* # [[Normality-largeness is transitive]]
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