LoadPackage("fga");; F:=FreeGroup(["x0","x1","x2"]);; co:=function(a,b) return a^-1*b^-1*a*b; end;; gf:=GeneratorsOfGroup(F);; x0:=gf[1];;x1:=gf[2];;x2:=gf[3];; x01:=GroupHomomorphismByImages(F,F,gf,[x1^-1*x0*x1,co(x1,x0)*x1,x2]); x02:=GroupHomomorphismByImages(F,F,gf,[x2^-1*x0*x2,x1*co(x1,co(x0,x2)),co(x2,x0)*x2]); x12:=GroupHomomorphismByImages(F,F,gf,[x0,x2^-1*x1*x2,co(x2,x1)*x2]); N:=FreeGroup(["a","b0","b1","b2","c0","c1","c2"]);; H:=Group([x0^3,x1,x0^-1*x1*x0,x0^-2*x1*x0^2,x2,x0^-1*x2*x0,x0^-2*x2*x0^2]); phi:=GroupHomomorphismByImages(N,H,GeneratorsOfGroup(N),GeneratorsOfGroup(H)); o:=Image(x02^3,x1);; PreImagesRepresentative(phi,o);