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#### Article Title

Invariants of Finite Groups Acting as Flag Automorphisms

#### Abstract

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.

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