IA automorphism

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In mathematics, in the realm of group theory, an IA automorphism of a group is an automorphism that acts as identity on the abelianization. The abelianization of a group is its quotient by its commutator subgroup. An IA automorphism is thus an automorphism that sends each coset of the commutator subgroup to itself.

The IA automorphisms of a group form a subgroup of the automorphism group. Every inner automorphism, and more generally every extensible automorphism, is an IA automorphism.