Groupprops, The Group Properties Wiki (pre-alpha)
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IA-automorphism-invariant subgroup
From Groupprops
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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof.
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Definition
A subgroup of a group is termed an IA-automorphism-invariant subgroup if it is invariant under all IA-automorphisms of the whole group.
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
The property of being an IA-automorphism-invariant subgroup is the invariance property with respect to IA-automorphisms, and has the function restriction expression:
IA-automorphism 
Function
In particular, it is an endo-invariance property with function restriction expression:
IA-automorphism Endomorphism
In fact, since inverses of IA-automorphisms are IA-automorphisms, it is an auto-invariance property with function restriction expression:
IA-automorphism Automorphism
Relation with other properties
Stronger properties
Weaker properties
