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]


A subgroup H of a group G is termed a strongly image-potentially characteristic subgroup if there exists a surjective homomorphism \rho:K \to G such that both the kernel of \rho and \rho^{-1}(H) are characteristic subgroups of K.

Relation with other properties

Stronger properties

Weaker properties