Projectivity-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]
This is a variation of characteristic subgroup|Find other variations of characteristic subgroup | Read a survey article on varying characteristic subgroup

Definition

A subgroup of a group is termed projectivity-invariant if it is invariant under every projectivity of the group, i.e., every projectivity of the group maps the subgroup bijectively to itself.

Formalisms

Function restriction expression

This subgroup property is a function restriction-expressible subgroup property: it can be expressed by means of the function restriction formalism, viz there is a function restriction expression for it.
Find other function restriction-expressible subgroup properties | View the function restriction formalism chart for a graphic placement of this property

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Lattice automorphism-invariant subgroup invariant under all lattice automorphisms of the lattice of subgroups |FULL LIST, MORE INFO
Order-unique subgroup unique subgroup of its order |FULL LIST, MORE INFO
Projective-isomorph-free subgroup no other subgroup such that there is a projectivity between the two subgroups |FULL LIST, MORE INFO

Weaker properties

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