"Source: Text/Group/GrpFP.text";
"Line: 6485";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 6485
// Example: H80E50 ()
print "Example: H80E50";
ei := GetEchoInput();
SetEchoInput(true);
p4g<r, s> := FPGroup< r, s | r^2 = s^4 = (r*s^-1*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);
assert $1 eq 8;
Index(p4g, k);
assert $1 eq 8;
h eq k;
assert not $1;
IsNormal(p4g, h);
assert not $1;
IsNormal(p4g, k);
assert $1;
n := NormalClosure(p4g, h);
IsMaximal(p4g, n);
assert $1;
k subset n;
assert $1;
l := sub< p4g | (s*r)^4, s^-1*r >;
IsConjugate(p4g, h, l);
h meet l eq Core(p4g, h);
assert $1;
SetEchoInput(ei);
