[[Fact about::Characteristic subgroup]][[Category:Subgroup property non-implications]]

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Characteristic direct factor not implies fully characteristic
Characteristic not implies I-characteristic
Characteristic not implies amalgam-characteristic
Characteristic not implies characteristic-isomorph-free
Characteristic not implies fully characteristic
Characteristic not implies fully characteristic in finite Abelian group
Characteristic not implies fully characteristic in finitely generated Abelian group
Characteristic not implies strictly characteristic
Nilpotent not implies ACIC
Normal not implies characteristic
P-automorphism-invariant not implies characteristic

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