Group in which every normal subgroup is powering-invariant

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Definition

A group in which every normal subgroup is powering-invariant is a group in which every normal subgroup is a powering-invariant subgroup.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
group in which every subgroup is powering-invariant				|FULL LIST, MORE INFO
finite group		(via every subgroup is powering-invariant)	(via every subgroup is powering-invariant)	|FULL LIST, MORE INFO
periodic group		(via every subgroup is powering-invariant)	(via every subgroup is powering-invariant) -- explicitly, any aperiodic abelian group such as the group of rational numbers	|FULL LIST, MORE INFO
simple group				|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
group in which every characteristic subgroup is powering-invariant	every characteristic subgroup is powering-invariant	follows from characteristic implies normal	the group of rational numbers is a counterexample	|FULL LIST, MORE INFO