"Source: Text/Group/GrpFPInt.text";
"Line: 1601";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFPInt.text, line: 1601
// Example: H79E19 ()
print "Example: H79E19";
ei := GetEchoInput();
SetEchoInput(true);
p4g<r, s> := FPGroup< r, s | r^2 = s^4 = (r,s)^2 = 1 >;
h := sub< p4g | (s^-1*r)^4, s*r >;
k := sub< p4g | (s^-1*r)^2, (s*r)^2 >;
Index(p4g, h), Index(p4g, k);
h eq k;
IsConjugate( p4g, h, k); 
IsNormal(p4g, h), IsNormal(p4g, k);
n := NormalClosure(p4g, h);
IsMaximal(p4g, n);
k subset n;
l := sub< p4g | (s*r)^4, s^-1*r >;
IsConjugate(p4g, h, l);
(h meet l) eq Core(p4g, h);
SetEchoInput(ei);
