Semi-strongly image-potentially characteristic 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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This term is related to: NIPC conjecture
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Definition

A subgroup $H$ of a group $G$ is termed a semi-strongly image-potentially characteristic subgroup if there exists a group $K$ with a surjective homomorphism $\rho:K \to G$ such that $\rho^{-1}(H)$ is a characteristic subgroup of $K$.

Relation with other properties

Stronger properties

• Characteristic subgroup
• Kernel of a characteristic action on an abelian group
• Strongly image-potentially characteristic subgroup

Weaker properties

• Image-potentially characteristic subgroup
• Normal subgroup