# Semi-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]
This term is related to: NIPC conjecture
View other terms related to NIPC conjecture | View facts related to NIPC conjecture

## 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 $K$.