Isomorph-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: isomorph-automorphic subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup of a group is termed an isomorph-automorphic normal subgroup if it satisfies the following two conditions:

  1. It is a normal subgroup.
  2. Every subgroup of the whole group isomorphic to it is an automorphic subgroup, i.e., there is an automorphism sending one subgroup to the other.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Isomorph-free subgroup No other isomorphic subgroup (see also list of examples)
Order-automorphic normal subgroup

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Isomorph-normal subgroup every isomorphic subgroup of whole group is normal isomorph-normal not implies isomorph-automorphic (see also list of examples)
Isomorph-automorphic subgroup
Normal subgroup