# HEP-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 HEP-subgroup or is said to have the Homomorphism Extension Property if, for any homomorphism of groups $\varphi:H \to G$, there exists an endomorphism $\varphi'$ of $G$ such that the restriction of $\varphi'$ to $H$ equals $\varphi$.