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説明
AbstractLet K be an algebraic number field, of degree n, with a completely ramifying prime p, and let t be a common divisor of n and (p − 1)2. Then it is proved that if K does not contain the unique subfield, of degree t, of the p-th cyclotomic number field, then we have (hK, n) > 1, where hK is the class number of K. As applications, we give several results on hK of such algebraic number fields K.
収録刊行物
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- Journal of Number Theory
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Journal of Number Theory 2 404-413, 1970-11-01
Elsevier BV
