Quotientable automorphism

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In mathematics, in the realm of group theory, a quotientable automorphism of a group is an automorphism that takes every normal subgroup to within itself. As a result, it gives a corresponding automorphism for every quotient group.

Quotientable automorphisms possess the following properties:

• Every inner automorphism is quotientable. More generally, any automorphism defined by an algebraic formula is quotientable.
• Every class automorphism and every family automorphism is quotientable.
• Every power automorphism is quotientable.
• Normal subgroups can be characterized as subgroups invariant under quotientable automorphisms.