# Isomorph-dominating subgroup

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]

## Contents

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

## Definition

A subgroup $H$ of a group $G$ is termed an isomorph-dominating subgroup if, for any subgroup $K$ of $G$ such that $H$ and $K$ are isomorphic groups, $K$ is contained in a conjugate subgroup of $H$, i.e., there exists $g \in G$ such that $K \le gHg^{-1}$.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
homomorph-dominating subgroup every homomorphic image is contained in a conjugate |FULL LIST, MORE INFO