Under a group homomorphism, the image of the inverse is the inverse of the image

https://arbital.com/p/group_homomorphism_image_of_inverse

by Patrick Stevens Jun 14 2016 updated Jun 14 2016

The operations of "taking inverses" and "applying a group homomorphism" commute: it does not matter in which order we do them.


For any Group homomorphism , we have .

Indeed, , and similarly for multiplication on the left.