Lattice automorphism-invariant 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]
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Definition

A subgroup of a group is termed a lattice automorphism-invariant subgroup if it is invariant under all the lattice automorphisms of the lattice of subgroups of the group.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Projectivity-invariant subgroup invariant under every projectivity |FULL LIST, MORE INFO
Characteristic subgroup invariant under all automorphisms Projectivity-invariant subgroup|FULL LIST, MORE INFO
Normal subgroup invariant under all inner automorphisms Projectivity-invariant subgroup|FULL LIST, MORE INFO