[GAP Forum] Group[HomomorphismByImages

[Abdulhakeem Olayiwola]

Thank you for the clarification.

On Jul 6, 2017 9:54 AM, <dmitrii.pasechnik at cs.ox.ac.uk> wrote:

> Dear Abdulhakeem,
> > Please can someone explain the reason why i am having this error; and a
> > possible solution.
>
> > gap> f:=FreeGroup("a","b");
> > gap> a:=f.1; b:=f.2;
> > gap>  rel:=[a^4,b^2,b^-1*a*b*a];
> > gap> D8:=f/rel;
> > gap> SetReducedMultiplication(D8);
> > gap> A:=AutomorphismGroup(D8);
> > gap> List(A);
> [...]
> > gap> f1:=GroupHomomorphismByImages(D8,D8, [ b, b*a^2, a*b ] -> [ b,
> b*a^2,
> > a*b ]);
>
> First of all, a and b are not elements of D8, they are elements of f,
> the free group.  So you'd first need to do, after defining D8,
>
> a:=D8.1;
> b:=D8.2;
>
> (or, perhaps, other variable names, for clarity, etc)
>
> Then,  [ b, b*a^2, a*b ] -> [ b, b*a^2, > a*b ] is not valid GAP syntax,
> and anyway this is not what GroupHomomorphismByImages expects as input;
> instead
>
> f1:=GroupHomomorphismByImages(D8,D8, [ b, b*a^2, a*b ],[ b, b*a^2, a*b ]);
>
> will to the job.
>
> Hope this helps,
> Dima
>
>