# Isomorph-free subgroup of group of prime power order

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: isomorph-free subgroup with a group property imposed on theambient group: group of prime power order

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Statement

An **isomorph-free subgroup of group of prime power order** is a subgroup of a group where the group is a group of prime power order and the subgroup is an isomorph-free subgroup.

## Relation with other properties

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

characteristic subgroup of group of prime power order | the group is a group of prime power order and the subgroup is a characteristic subgroup | follows from isomorph-free implies characteristic | See prime power order examples in characteristic not implies isomorph-free | Isomorph-normal characteristic subgroup of group of prime power order|FULL LIST, MORE INFO |

normal subgroup of group of prime power order | the group is a group of prime power order and the subgroup is a normal subgroup | Characteristic subgroup of group of prime power order, Isomorph-normal characteristic subgroup of group of prime power order, Isomorph-normal subgroup of group of prime power order, Sylow-relatively weakly closed subgroup|FULL LIST, MORE INFO |