IA_automorphism

IA automorphism

IA automorphism

Add article description

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.

See also

References

  1. [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.


Stub icon

This group theory-related article is a stub. You can help Wikipedia by expanding it.
Share this article:

This article uses material from the Wikipedia article IA_automorphism, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.