[GAP Forum] Displayed name for generators of group

[Hulpke,Alexander]

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