On Totally Real Hilbert - Speiser Fields of Type
نویسنده
چکیده
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 OL is free as an OKG-module. Let Cp 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 Cp.
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Let G be a finite abelian group. A number field K is called a Hilbert-Speiser field of type G if every tame G-Galois extension L/K has a normal integral basis, i.e., the ring of integers OL is free as an OKG-module. Let Cp 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-Sp...
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تاریخ انتشار 2009