# Difference between revisions of "Homomorph-containing 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 homomorph-containing if for any $\varphi \in \operatorname{Hom}(H,G)$, the image $\varphi(H)$ is contained in $H$.