"Source: Text/Group/GrpFP.text";
"Line: 7007";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 7007
// Example: H80E53 ()
print "Example: H80E53";
ei := GetEchoInput();
SetEchoInput(true);
B := BraidFPGroup(5);
B;
S := Sym(5);
imgs := [ S!(1,2), S!(2,3), S!(3,4), S!(4,5) ];
rels := Relations(B);
rels;
IsSatisfied(rels, imgs);
assert $1;
f := hom< B->S | imgs >;
f(B) eq S;
assert $1;
Kernel(f);
GeneratingWords(B, Kernel(f));
Kernel(f) eq ncl< B | B.1^2, B.2^2, B.3^2, B.4^2 >;
assert $1;
SetEchoInput(ei);
