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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Sur le rang du $2$-groupe de classes de $Q({\sqrt{m}},{\sqrt{d}})$$m=2$ ou un premier $p\equiv 1\,(mod\,4)$


Authors: Abdelmalek Azizi and Ali Mouhib
Journal: Trans. Amer. Math. Soc. 353 (2001), 2741-2752
MSC (2000): Primary 11R16, 11R29, 11R37
Published electronically: February 7, 2001
MathSciNet review: 1828471
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Abstract:

On the rank of the $2$-class group of $Q({\sqrt{m}},{\sqrt{d}})$. Let $d$ be a square-free positive integer and $p$ be a prime such that $p\equiv 1\,(mod\, 4)$. We set $K = Q({\sqrt{m}},{\sqrt{d}})$, where $m=2$ or $m=p$. In this paper, we determine the rank of the $2$-class group of $K$.

RÉSUMÉ. Soit $K = Q({\sqrt{m}},{\sqrt{d}})$, un corps biquadratique où $m=2$ ou bien un premier $p\equiv 1\,(mod\,4)$ et $d$ étant un entier positif sans facteurs carrés. Dans ce papier, on détermine le rang du $2$-groupe de classes de $K$.


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Additional Information

Abdelmalek Azizi
Affiliation: Département de Mathématiques, Faculté des Sciences, Université Mohammed 1, Oujda, Maroc
Email: azizi@sciences.univ-oujda.ac.ma

Ali Mouhib
Affiliation: Département de Mathématiques, Faculté des Sciences, Université Mohammed 1, Oujda, Maroc

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02753-2
PII: S 0002-9947(01)02753-2
Received by editor(s): October 13, 1999
Received by editor(s) in revised form: July 8, 2000
Published electronically: February 7, 2001
Article copyright: © Copyright 2001 American Mathematical Society