Unipotent automorphism-invariant subgroup

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 unipotent automorphism-invariant subgroup if it is invariant under all unipotent 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.
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The property of being unipotent automorphism-invariant can be expressed as the invariance property:

Unipotent automorphism $\to$ Function

It is in fact an endo-invariance property:

Unipotent automorphism $\to$ Endomorphism

Because the inverse of a unipotent automorphism is unipotent, it can in fact be expressed as an auto-invariance property:

Unipotent automorphism $\to$ Automorphism

Finally, since the property of being unipotent is preserved under restricting the action to a subgroup, it can be expressed as a balanced subgroup property (function restriction formalism):

Unipotent automorphism $\to$ Unipotent automorphism

Relation with other properties

Stronger properties

• Characteristic subgroup