Class numbers of pure fields
Author:
R. A. Mollin
Journal:
Proc. Amer. Math. Soc. 98 (1986), 411414
MSC:
Primary 11R29; Secondary 11R21, 11R32
MathSciNet review:
857932
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Abstract: Necessary and sufficient conditions are given for the class number of a pure field to be divisible by for a given positive integer and prime . Moreover the divisibility of by is linked with the rank of the class group of the and prime divisors of , where is a primitive th root of unity. Finally we prove in an easy fashion that for a given odd prime and any natural number there exist infinitely many nonGalois algebraic number fields (in fact pure fields) of degree over whose class numbers are all divisible by .
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 C. D. Walter, Pure fields of degree 9 with class number prime to 3, Ann. Inst. Fourier Grenoble 30 (1980), 115. MR 584268 (82b:12006)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198608579322
PII:
S 00029939(1986)08579322
Article copyright:
© Copyright 1986 American Mathematical Society
