On an equation with dihedral Galois group

An earlier result of the author is applied to the inverse Galois problem for the dihedral group of odd order. The solution is given in the form of a polynomial in one variable. A completeness theorem holds for this polynomial; this means that any solution is determined by such a polynomial. Under natural assumptions concerning the ground field, necessary and sujfficient conditions of irreducibility of these polynomials are given and some properties of these polynomials are proved. The problem of classification of cubic irrationalities with respect to the Tchirngausen transformations is completely solved. Bibliography: 5 titles.