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The exponent three class group problem for some real cyclic cubic number fields


Author: Stéphane Louboutin
Journal: Proc. Amer. Math. Soc. 130 (2002), 353-361
MSC (1991): Primary 11R16, 11R29, 11R42
DOI: https://doi.org/10.1090/S0002-9939-01-06168-8
Published electronically: June 8, 2001
MathSciNet review: 1862112
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Abstract:

We determine all the simplest cubic fields whose ideal class groups have exponent dividing $3$, thus generalizing the determination by G. Lettl of all the simplest cubic fields with class number $1$ and the determination by D. Byeon of all all the simplest cubic fields with class number $3$. We prove that there are $23$ simplest cubic fields with ideal class groups of exponent $3$ (and $8$ simplest cubic fields with ideal class groups of exponent $1$, i.e. with class number one).


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Additional Information

Stéphane Louboutin
Affiliation: Institut de Mathématiques de Luminy, UPR 906, 163, avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France
Email: loubouti@iml.univ-mrs.fr

DOI: https://doi.org/10.1090/S0002-9939-01-06168-8
Keywords: Simplest cubic field, cubic field, class number, class group
Received by editor(s): June 26, 2000
Published electronically: June 8, 2001
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2001 American Mathematical Society

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