IA automorphism

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.

References

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.