"Source: Text/RepThy/ModAlg.text";
"Line: 3698";
"Date: Fri Sep 26 12:10:12 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/RepThy/ModAlg.text, line: 3698
// Example: H99E24 ()
print "Example: H99E24";
ei := GetEchoInput();
SetEchoInput(true);
SetSeed(1);
M := PermutationModule(CyclicGroup(6), GF(3));
L := SubmoduleLattice(M);
#L;
assert $1 eq 16;
T := Top(L);
B := Bottom(L);
T;
B;
// Check that element of L corresponding to M is T
L ! M;
(L ! M) eq T;
assert $1;
// Check that module corresponding to B is zero-submodule of M
Module(B);
S := MinimalSupermodules(B);
S;
Module(L ! 2);
Module(L ! 3);
Dimension(L ! 2);
assert $1 eq 1;
Morphism(L ! 2);
Morphism(L ! 3);
// Set A to the sum of these elements
A := L!2 + L!3;
A;
// Note that A has dimension 2 and its morphism is the sum of the previous
Dimension(A);
assert $1 eq 2;
Morphism(A);
MaximalSubmodules(A);
S!2 subset A;
assert $1;
MaximalSubmodules(T);  
A := L ! 14;
Dimension(A);   
assert $1 eq 5;
Morphism(A);
S := Module(A);
S;
J := JacobsonRadical(S);
J;
L ! J;
JacobsonRadical(A);
assert $1 eq $2;
SetEchoInput(ei);
