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.[1] 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 normal subgroup of the automorphism group. Every inner automorphism is an IA automorphism.


  1. ^ Bachmuth, S. (1966), "Induced automorphisms of free groups and free metabelian groups", Transactions of the American Mathematical Society, 122: 1–17, doi:10.2307/1994498, MR 0190212.