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On a Theorem of Lenstra and Schoof

B. V. Petrenko
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Abstract

We give a detailed proof of Theorem 1.15 from a well-known paper "Primitive normal bases for finite fields" by H.W. Lenstra Jr. and R.J. Schoof. We are not aware of any other proofs. Let $L/K$ be a finite-dimensional Galois field extension and $B$ the set of all normal bases of this extension. Theorem 1.15 describes the group of all $γ$ in the multiplicative group of $L$ such that $γB = B$.

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B. V. Petrenko. 2002-09-10. On a Theorem of Lenstra and Schoof. https://arxiv.org/abs/math/0209106

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