[GAP Forum] Is there a way to teach GAP that a particular map is injective or surjective?

[Hulpke,Alexander]

Dear Forum,

> On Jan 15, 2019, at 3:26 PM, Will Chen <oxeimon at gmail.com> wrote:
> 
> Dear Forum,
> 
> Suppose I have two groups G, H, and a homomorphism f : G --> H, defined
> using "GroupHomomorphismByImages".
> 
> Suppose I know that f is surjective, and that moreover there is a
> generating set X of H for which I can provide explicit preimages in G.
> 
> Is there a way of giving GAP this information?

You can use

SetIsInjective(map,true) and SetIsSurjective(map,true).

You also might want to use PreImagesRepresentative instead of PreImage.

Then is f is given on pre-images of X with image set X, and H is finitely presented, GAP should be able to calculate such pre-images for arbitrary elements.

All the best,

  Alexander Hulpke