Class numbers of pure fields

Author:
R. A. Mollin

Journal:
Proc. Amer. Math. Soc. **98** (1986), 411-414

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 non-Galois algebraic number fields (in fact pure fields) of degree over whose class numbers are all divisible by .

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1986-0857932-2

Article copyright:
© Copyright 1986
American Mathematical Society