A generalization of Hubert’s theorem 94
1991 ◽
Vol 121
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pp. 161-169
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In this paper we shall prove the following theorem conjectured by Miyake in [3] (see also Jaulent [2]).THEOREM. Let k be a finite algebraic number field and K be an unramified abelian extension of k, then all ideals belonging to at least [K: k] ideal classes of k become principal in K.Since the capitulation homomorphism is equivalently translated to a group-transfer of the galois group (see Miyake [3]), it is enough to prove the following group-theoretical verison:
1957 ◽
Vol 12
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pp. 177-189
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1961 ◽
Vol 19
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pp. 169-187
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2010 ◽
Vol 06
(06)
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pp. 1273-1291
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1984 ◽
Vol 93
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pp. 133-148
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1978 ◽
Vol 70
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pp. 183-202
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1967 ◽
Vol 29
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pp. 281-285
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1991 ◽
Vol 67
(2)
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pp. 55-59
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