Group automorphisms | Group theory

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. 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. (Wikipedia).

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Related pages

Normal subgroup | Quotient group | Mathematics | Commutator subgroup | Coset | Group theory | Automorphism | Inner automorphism | Group (mathematics)