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IA-automorphism-balanced subgroup

Definition

A subgroup of a group is termed an IA-automorphism-balanced subgroup or IA-balanced subgroup if every IA-automorphism of the whole group restricts to an IA-automorphism of the subgroup.

Formalisms

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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
Function restriction expression H is an IA-automorphism-balanced subgroup of G if ... This means that being IA-automorphism-balanced is ... Additional comments
IA-automorphism \to IA-automorphism every IA-automorphism of G restricts to a IA-automorphism of H the balanced subgroup property for IA-automorphisms Hence, it is a t.i. subgroup property, both transitive and identity-true

Relation with other properties

Metaproperties