Let K be a field and suppose that G is a finite group that acts faithfully on $(x1,...,xm) by automorphisms of the form g(xi)=ai(g)xi+bi(g), where ai(g),bi(g) \in K(x1,...,xi-1) for all g \in G and all i=1,...,m. As shown by Miyata, the fixed field K(x1,...,xi-1)G is purely transcendental over K and admits a transcendence basis {\phi1,...,\phim}, where \phii is in K(x1,...,xi-1) [xi]G and has minimal positive degree di in xi. We determine exactly the degree di of each invariant \phii as a polynomial in xi and show the relation d1 ... dm=|G|. As an application, we compute a generic polynomial for the dihedral group D8 of order 16 in characteristic 2.

Author Bio

Dennis Tseng grew up in Cincinnati, Ohio where he attended William Mason High. He is currently a sophomore math major at MIT. The submitted work was done in the summer after his freshman year. He plans to attend graduate school in mathematics.