Finite-iteratively extensible automorphism

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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This is a variation of extensible automorphism|Find other variations of extensible automorphism |

This term is related to: Extensible automorphisms problem
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Definition

An automorphism of a group is said to be finite-iteratively extensible if it is $\alpha$-extensible (refer iteratively extensible automorphism) for every natural number (or finite ordinal) $\alpha$.

Relation with other properties

Stronger properties

• Inner automorphism
• Infinity-extensible automorphism

Weaker properties

• Finite-chain-extensible automorphism
• Extensible automorphism