Order-automorphic normal subgroup
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: order-automorphic subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties
Definition
A subgroup of a group is termed an order-automorphic normal subgroup if it satisfies the following two conditions:
- It is a normal subgroup.
- it is an order-automorphic subgroup, i.e., any subgroup of the same order is an automorphic subgroup.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Order-unique subgroup |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Order-automorphic subgroup | ||||
| Normal subgroup | ||||
| Order-normal subgroup | ||||
| Order-isomorphic normal subgroup | ||||
| Order-isomorphic subgroup | ||||
| Isomorph-automorphic normal subgroup | ||||
| Isomorph-normal subgroup |