# Isomorph-commensurable 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 is a variation of isomorph-free subgroup|Find other variations of isomorph-free subgroup |

## Definition

### Symbol-free definition

A subgroup of a group is termed an isomorph-commensurable subgroup if it is commensurable with all subgroups of the group isomorphic to it.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Subgroup of finite group
Finite subgroup
Isomorph-free subgroup no other isomorphic subgroup

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Automorph-commensurable subgroup commensurable with all automorphic subgroups
Conjugate-commensurable subgroup commensurable with all conjugate subgroups