[GAP Forum] Displayed name for generators of group

[Gabriel Cardona]

It will do the trick... Thanks a lot!
Biel

On Mon, Sep 3, 2018 at 7:15 PM Hulpke,Alexander <
Alexander.Hulpke at colostate.edu> wrote:

> Dear Forum, Dear Gabriel Cardona,
>
> > I am trying to display the elements of a group using names that I specify
> > for the generators. I could find a way to do it when the group is given
> as
> > generators and relations, but not when it is constructed with
> DirectProduct
> > (or CyclicGroup,...).
> >
> > A simplified example is as follows:
> >
> > gap> F1:=FreeGroup("s");;
> > gap> G1:=F1/[F1.1^2];;
> > gap> F2:=FreeGroup("t");;
> > gap> G2:=F2/[F2.1^2];;
> > gap> G:=DirectProduct(G1,G2);;
> > gap> Elements(G1);
> > [ <identity ...>, s ]
> > gap> Elements(G2);
> > [ <identity ...>, t ]
> > gap> Elements(G);
> > [ <identity ...>, f1, f2, f1*f2 ]
> >
> > I would like to get "f1" displayed as "s" and "f2" as "t".
> > Is there a way to do it?
>
> At this point, `DirectProduct` simply creates new generators named
> consecutively without an option to rename.
>
> The only thing you could do is to create a new finitely presented group
> with differehtly named generators and copying over the relators. In your
> example:
>
> new:=FreeGroup("s","t");
> newrel:=List(RelatorsOfFpGroup(G),
> x->MappedWord(x,FreeGeneratorsOfFpGroup(G),GeneratorsOfGroup(new)));
> GG:=new/newrel;
>
> Alas this new group will lose the direct product information that would
> allow for projections etc., so it is only a partial solution. I'll see
> whether one could preserve existing names.
>
> Regards,
>
>    Alexander Hupke
>
>
>
>