Normal-potentially fully invariant subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

A subgroup $H$ of a group $G$ is termed a normal-potentially fully invariant subgroup of $G$ if there exists a group $K$ containing $G$ as a normal subgroup, such that $H$ is a fully invariant subgroup of $K$.

Formalisms

In terms of the normal-potentially operator

This property is obtained by applying the normal-potentially operator to the property: fully invariant subgroup
View other properties obtained by applying the normal-potentially operator

Relation with other properties

Stronger properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Fully invariant subgroup				|FULL LIST, MORE INFO
Central subgroup of finite group				|FULL LIST, MORE INFO
Normal-potentially verbal subgroup				|FULL LIST, MORE INFO
Fully invariant-potentially fully invariant subgroup				|FULL LIST, MORE INFO

Weaker properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Potentially fully invariant subgroup				|FULL LIST, MORE INFO
Normal-potentially characteristic subgroup				|FULL LIST, MORE INFO
Normal subgroup				|FULL LIST, MORE INFO