IJPAM: Volume 103, No. 1 (2015)

THE GENERATORS OF THE $2$-CLASS GROUP OF
SOME FIELDS $\QQ(\sqrt{pq_1q_2}, i)$:
CORRECTION TO THEOREM 3 OF [5]

Abdelmalek Azizi$^1$, Abdelkader Zekhnini$^2$, Mohammed Taous$^3$
$^1$Department of Mathematics
Faculty of Sciences
Mohammed First University
Oujda, MOROCCO
$^2$Department of Mathematics
Pluridisciplinary Faculty
Mohammed First University
Nador, MOROCCO
$^3$Department of Mathematics
Faculty of Science and Technology
Moulay Ismail University
Errachidia, MOROCCO


Abstract. Let $p$, $q_1$ and $q_2$ be different primes satisfying the condition that the 2-class group of the fiel $\mathds{k}=\QQ\left(\sqrt{pq_1q_2}, i\right)$ is of type (2, 2, 2). In this paper, we are interested to give the generators of $\mathbf{C}_{\mathds{k}, 2}$, the $2$-class group of $\mathds{k}$, which corrects the Theorem 3 of A. Azizi, A. Zekhnini and M. Taous: On the generators of the $2$-class group of the field $\mathbf{k}=\QQ(\sqrt{d}, i)$, IJPAM, Volume 81, No. 5 (2012), 773-784.

Received: March 31, 2015

AMS Subject Classification: 11R11, 11R29, 11R32, 11R37

Key Words and Phrases: $2$-class group, class group, biquadratic field, Hilbert class field

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DOI: 10.12732/ijpam.v103i1.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 1
Pages: 99 - 107


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