Normal-isomorph-free subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup of a group is termed normal-isomorph-free if it is a normal subgroup, and there is no other normal subgroup of the whole group isomorphic to it.

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 |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Normal-isomorph-containing subgroup contains any isomorphic normal subgroup of whole group |FULL LIST, MORE INFO
Characteristic-isomorph-free subgroup characteristic and no isomorphic characteristic subgroup |FULL LIST, MORE INFO
Characteristic subgroup invariant under all automorphisms Characteristic-isomorph-free subgroup, Series-isomorph-free subgroup|FULL LIST, MORE INFO
Series-isomorph-free subgroup no other normal subgroup that is isomorphic and has isomorphic quotient |FULL LIST, MORE INFO
Normal-isomorph-automorphic subgroup normal and any isomorphic normal subgroup is automorphic |FULL LIST, MORE INFO