Normal-isomorph-automorphic 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

Definition with symbols

A subgroup H of a group G is termed a normal-isomorph-automorphic subgroup if H is a normal subgroup of G and for any normal subgroup K of G isomorphic to H, H and K are automorphic subgroups in G, i.e., there is an automorphism \sigma of G such that \sigma(H) = K.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Normal-isomorph-free subgroup normal, and no other isomorphic normal subgroup |FULL LIST, MORE INFO
Isomorph-free subgroup No other isomorphic subgroup (via normal-isomorph-free) (via normal-isomorph-free) Normal-isomorph-free subgroup|FULL LIST, MORE INFO
Isomorph-automorphic normal subgroup Normal, and automorphic to all isomorphic subgroups |FULL LIST, MORE INFO