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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A note on $ 1$-class groups of number fields


Author: Frank Gerth
Journal: Math. Comp. 29 (1975), 1135-1137
MSC: Primary 12A35; Secondary 12A50, 12A30
MathSciNet review: 0409406
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Abstract: Let F be a number field and K a cyclic extension of degree l over F, where l is a rational prime. The l-class group of K is analyzed as a $ {\operatorname{Gal}}(K/F)$-module in the case where the l-class group of F is trivial. The resulting structure theorem is used to compute the structure of the 3-class groups of certain cyclic cubic fields that are discussed in a paper of D. Shanks.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1975-0409406-1
PII: S 0025-5718(1975)0409406-1
Article copyright: © Copyright 1975 American Mathematical Society