Some Actions of Symmetrical Groups Original Research Article

Let K be any field, V the n-dimensional vector space over K, on which the symmetric group Sn acts by permuting a basis. Then the fixed fields K(SkV)Sn and K(logical and(k)V)Sn are rational over K where SkV and logical and(k)V are the kth symmetric power and exterior power of V respectively. The rationality of some other fixed fields are established also.