Group in which every characteristic 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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Definition

A group in which every characteristic subgroup is powering-invariant is a group in which every characteristic 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 Group in which every normal subgroup is powering-invariant|FULL LIST, MORE INFO
group in which every normal 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 normal 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 normal subgroup is powering-invariant, Group in which every subgroup is powering-invariant|FULL LIST, MORE INFO
abelian group characteristic subgroup of abelian group implies powering-invariant any finite non-abelian group will do |FULL LIST, MORE INFO
characteristically simple group |FULL LIST, MORE INFO
simple group (via characteristically simple) (via characteristically simple) Group in which every normal subgroup is powering-invariant|FULL LIST, MORE INFO

Incomparable properties

Conjecture

The conjecture that every characteristic subgroup of nilpotent group is powering-invariant is currently open. The conjecture states that the property of being a nilpotent group is stronger than the property of being a group in which every characteristic subgroup is powering-invariant.