Fully invariant-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 $K$ is termed a strongly potentially fully characteristic subgroup if there exists a group $G$ containing $K$ such that both $H$ and $K$ are fully invariant subgroups of $G$.

Relation with other properties

Stronger properties

• Fully invariant subgroup

Weaker properties

• Potentially fully invariant subgroup
• Normal subgroup