  The product formula of Artin symbols (norm residue symbols) is an important
equality that connects local and global class field theory. Usually, the
product formula of Artin symbols is considered in abelian extensions of global
fields. In this paper, however, the product is considered in non-abelian
extensions such that each symbol is well-defined. As an application, some
properties on fundamental units of real quadratic fields are obtained and will
be presented here.
