#Example: "EpimorphismStandardPresentation" . . . based on manual example
#(demonstrates `EpimorphismStandardPresentation' usage)
#vars: F, x, y, z, w, a, b, R, Q, procId, G, f1, f2, f3, f4, f5, f6, phi;
#options:
F := FreeGroup(6, "F");
## For printing GAP uses the symbols F1, ... for the generators of F
x := F.1; y := F.2; z := F.3; w := F.4; a := F.5; b := F.6;
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 ];
Q := F / R;
## For printing GAP also uses the symbols F1, ... for the generators of Q
## (the same as used for F) ... but the gen'rs of Q and F are different:
GeneratorsOfGroup(F) = GeneratorsOfGroup(Q);
#alt: do
#procId := PqStart( Q );
#alt: sub <procId> for <Q>
G := Pq( Q : Prime := 3, ClassBound := 3 );
#alt: sub <procId> for <Q>
phi := EpimorphismStandardPresentation( Q : Prime := 3,
ClassBound := 3 );
Source(phi); # This is the group Q (GAP uses F1, ... for gen'r symbols)
Range(phi); # This is the group G (GAP uses f1, ... for gen'r symbols)
AssignGeneratorVariables(G);; # so f1, ... are now variables
## Just to see that the images of [F1, ..., F6] do generate G
Group([ f1*f2^2*f3, f1*f2*f3*f4*f5^2*f6^2, f3^2, f4, f5, f6 ]) = G;
Size( Image(phi) );
¤ Dauer der Verarbeitung: 0.14 Sekunden
(vorverarbeitet)
¤
*© Formatika GbR, Deutschland
|
|
