57.7 IsomorphismPcpStandardPcp

IsomorphismPcpStandardPcp( G, S )

Let G be a p-group and let S be the standard presentation computed for G by StandardPresentation. IsomorphismPcpStandardPcp returns the isomorphism from G to S.

We illustrate the function with the following example.

    gap> F := FreeGroup (6);
    Group( f.1, f.2, f.3, f.4, f.5, f.6 )
    gap> x := F.1;; y := F.2;; z := F.3;; w := F.4;; a := F.5;; b := F.6;;
    gap> R := [x^3 / w, y^3 / w * a^2 * b^2, w^3 / b,
    >             Comm (y, x) / z, Comm (z, x), Comm (z, y) / a, z^3 ];;
    gap> q := F / R;;
    gap> G := Pq (q, "Prime", 3, "ClassBound", 3);
    Group( G.1, G.2, G.3, G.4, G.5, G.6 )
    gap> S := StandardPresentation (q, 3, "ClassBound", 3);
    Group( G.1, G.2, G.3, G.4, G.5, G.6 )
    gap> phi := IsomorphismPcpStandardPcp (G, S);
    GroupHomomorphismByImages( Group( G.1, G.2, G.3, G.4, G.5,
    G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
    [ G.1, G.2, G.3, G.4, G.5, G.6 ],
    [ G.1*G.2^2*G.3*G.4^2*G.5^2, G.1*G.2*G.3*G.5, G.3^2, G.4*G.6^2, G.5,
      G.6 ] ) 

This function requires the package "anupq" (see RequirePackage).

Previous Up Top Next
Index