Isomorph-normal characteristic 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-normal subgroup and characteristic subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

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

• It is characteristic in the whole group.
• It is isomorph-normal in the whole group: every subgroup of the group that is isomorphic to it is normal in the whole group.

Relation with other properties

Stronger properties

• Isomorph-free subgroup
• Isomorph-characteristic subgroup

Weaker properties

• Isomorph-normal subgroup
• Sub-(isomorph-normal characteristic) subgroup
• WNSCDIN-relatively weakly closed subgroup: For full proof, refer: Isomorph-normal characteristic of WNSCDIN implies weakly closed
• Characteristic subgroup
• Normal subgroup