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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Sur le rang du $2$-groupe de classes de $Q(\{\sqrt \{m\}\},\{\sqrt \{d\}\})$ où $m=2$ ou un premier $p\equiv 1(mod4)$
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by Abdelmalek Azizi and Ali Mouhib PDF
Trans. Amer. Math. Soc. 353 (2001), 2741-2752 Request permission

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
  • Received by editor(s): October 13, 1999
  • Received by editor(s) in revised form: July 8, 2000
  • Published electronically: February 7, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 2741-2752
  • MSC (2000): Primary 11R16, 11R29, 11R37
  • DOI: https://doi.org/10.1090/S0002-9947-01-02753-2
  • MathSciNet review: 1828471