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Minkowski units in a class of metabelian fields

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
37
Issue
1
Identifiers
DOI: 10.1016/s0022-314x(05)80025-3

Abstract

Let K be a normal real field with a metabelian Galois group G of order pm, where p is prime. This paper gives necessary conditions for K to have Minkowski units. The main condition is a relation bounding the class number of K and the class numbers of certain subfields of K. These conditions become sufficient when the class number of the maximal real subfield of the cyclotomic field Q( ζ p ) is one.

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