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

Author(s): Abdelmalek Azizi; Ali Mouhib
Journal: Trans. Amer. Math. Soc. 353 (2001), 2741-2752.
MSC (2000): Primary 11R16, 11R29, 11R37
Posted: February 7, 2001
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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: 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
Posted: February 7, 2001
Copyright of article: Copyright 2001, American Mathematical Society

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