"Source: Text/RepThy/ModAlg.text";
"Line: 3904";
"Date: Fri Sep 26 12:10:12 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/RepThy/ModAlg.text, line: 3904
// Example: H99E25 ()
print "Example: H99E25";
ei := GetEchoInput();
SetEchoInput(true);
G := PermutationGroup< 12 |
        (1,6,7)(2,5,8,3,4,9)(11,12),
        (1,3)(4,9,12)(5,8,10,6,7,11) >;
K := GF(3);
P := PermutationModule(G, K);
M := sub< P | [1,0,0,0,0,1,0,0,1,0,0,1] >;
M;
H := AHom(P, M);
H: Maximal;
// We write down a random homomorphism from M to P.
f := 2*H.1 + H.2;
f;
Ker := Kernel(f);
Ker;
Morphism(Ker, P);
// Examine the image of f and its morphism to P.
Im := Image(f);
Im;
Morphism(Im, P);
SetEchoInput(ei);
