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On a Theorem of Lenstra and Schoof | | B. V. Petrenko
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10 Sep 2002 | | Subject: | Number Theory; Rings and Algebras MSC-class: 12F10, 16K20, 20C05, 11T30, 12E20 | math.NT math.RA | | 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 $gamma$ in the multiplicative group of $L$ such that $gamma B = B$. | | Source: | arXiv, math.NT/0209106 | | Services: | Forum | Review | PDF | Favorites | |
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