Finite-iteratively extensible automorphism

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) $$\alpha$$.

Stronger properties

 * Weaker than::Inner automorphism
 * Weaker than::Infinity-extensible automorphism

Weaker properties

 * Stronger than::Finite-chain-extensible automorphism
 * Stronger than::Extensible automorphism