Group in which every normal subgroup is powering-invariant

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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) Group in which 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 Group in which every subgroup is powering-invariant|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