# Strongly image-potentially characteristic subgroup

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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]

## Definition

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 $K$.