Order-automorphic normal subgroup

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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:

  1. It is a normal subgroup.
  2. 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