[GAP Forum] transfer fp relators

[Max Horn]

Dear Rudolf Zlabinger,

the following program performs what you want in a reasonably simple and
extensible fashion.

f:=FreeGroup(4);;
s3:=SymmetricGroup(3);
a4:=AlternatingGroup(4);;
s3fp:=Image(IsomorphismFpGroup(s3));;
a4fp:=Image(IsomorphismFpGroup(a4));;

s3rels:=List(RelatorsOfFpGroup(s3fp), r->MappedWord(r,
FreeGeneratorsOfFpGroup(s3fp), [f.1,f.2]));;
a4rels:=List(RelatorsOfFpGroup(a4fp), r->MappedWord(r,
FreeGeneratorsOfFpGroup(a4fp), [f.3,f.4]));;
commrels:=ListX([f.1,f.2], [f.3,f.4], Comm);;

dirprodfp:= f / Union(s3rels, a4rels,commrels);;
dirprod:=DirectProduct(s3,a4);;
IsomorphismGroups(dirprodfp,dirprod);


Best regards,
Max