"Source: Text/Group/GrpFPInt.text";
"Line: 1997";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFPInt.text, line: 1997
// Example: H79E24 ()
print "Example: H79E24";
ei := GetEchoInput();
SetEchoInput(true);
B<x,y,z,t> := 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));
N := sub< B | x^2, y^2, z^2, t^2 >;
Kernel(f) eq NormalClosure(B, N);
assert $1;
BS := quo< B | x^2, y^2, z^2, t^2 >;
Order(BS);
P := PermutationGroup(BS);
P;
IsIsomorphic(P, Sym(5));
SetEchoInput(ei);
