public static bool IsNormal(Group <T> group, FiniteSet <T> subset)
{
foreach (T g in group.Set)
{
T inverse = group.Inverse(g);
foreach (T n in subset)
{
if (!subset.IsMember(group.Product(group.Product(g, n), inverse)))
{
return(false);
}
}
}
return(true);
}
public bool IsSubsetOf(FiniteSet <T> superset)
{
if (superset is FiniteSet <T> )
{
return(_set.IsSubsetOf(((FiniteSet <T>)superset)._set));
}
else
{
foreach (T element in _set)
{
if (!superset.IsMember(element))
{
return(false);
}
}
return(true);
}
}
public static bool IsSubgroup(Group <T> group, FiniteSet <T> subset)
{
if (!subset.IsSubsetOf(group.Set))
{
return(false);
}
foreach (T a in subset)
{
foreach (T b in subset)
{
T inverse = group.Inverse(b);
if (!subset.IsMember(group.Product(a, inverse)))
{
return(false);
}
}
}
return(true);
}