Groupprops, The Group Properties Wiki (pre-alpha)

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From Groupprops

NPC theorem

Fact about	Normal subgroup +
Modification dateThis property is a special property in this wiki.	22 September 2009 13:43:23  +
Uses	Characteristicity is centralizer-closed +
Categories	Proofs of equivalence of definitions

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Abelian implies every subgroup is potentially characteristic +, Central implies potentially characteristic +, Finite NPC theorem +, Finite normal implies potentially characteristic +, Kernel of a characteristic action on an abelian group with which it is characteristic in the direct product implies potentially characteristic +, Nilpotent implies every normal subgroup is potentially characteristic +, No nontrivial abelian normal p-subgroup for some prime p implies every p-divisible normal subgroup is potentially characteristic +, Normal subgroup contained in hypercenter is potentially characteristic +, Periodic normal implies potentially characteristic +	Fact related to
Every nontrivial normal subgroup is potentially characteristic-and-not-fully invariant +	Stronger than
Destroying outer automorphisms +	Survey article about
Characteristic-potentially characteristic subgroup +	Term related to
Characteristic not implies potentially fully invariant +, Every nontrivial normal subgroup is potentially characteristic-and-not-intermediately characteristic +	Uses

 

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