On totally real Hilbert-Speiser Fields of type C_p

Details On totally real Hilbert-Speiser Fields of type C_p On totally real Hilbert-Speiser Fields of type C_p

2008-06-02

arxiv.org/abs/0806.0258v3

Mathematics

Number Theory

8 pages, latex, minor revisions following referee's report

Scientific paper

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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