"Source: Text/Group/GrpFP.text";
"Line: 6505";
"Date: Mon May 17 16:13:13 2021";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Group/GrpFP.text, line: 6505
// Example: H78E50 ()
print "Example: H78E50";
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);
