Orbits of normal basis generators
Bogdan V. Petrenko · The Quarterly Journal of Mathematics · 2004
Let L/K be a finite‐dimensional Galois field extension with Galois group G, B the set of normal basis generators for this extension, and C={γ ∈L∣γ B=B}. Then C is a group under multiplication. This group was introduced and characterized in Theorem 1.15 of a well‐known paper ‘Primitive normal bases for finite fields’ by H. W. Lenstra Jr. and R. J. Schoof. This result was stated in that paper without a proof. The purpose of this paper is to give a proof of the theorem.