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arXiv · 0806.0258

On totally real Hilbert-Speiser Fields of type C_p

Cornelius Greither·Henri Johnston
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Abstract

Let G be a finite abelian group. A number field K is called a Hilbert-Speiser field of type G if for every tame G-Galois extension L/K has a normal integral basis, i.e., the ring of integers O_L is free as an O_K[G]-module. Let C_p denote the cyclic group of prime order p. We show that if p >= 7 (or p=5 and extra conditions are met) and K is totally real with K/Q ramified at p, then K is not Hilbert-Speiser of type C_p.

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Cornelius Greither, Henri Johnston. 2009-02-26. On totally real Hilbert-Speiser Fields of type C_p. https://doi.org/10.4064/aa138-4-3

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