Affiliation:
1. Moulay Ismail University of Meknes , Faculty of Sciences and Technology , P.O. Box 509-Boutalamine, 52 000 , Errachidia , Morocco
Abstract
Abstract
Let K = ℚ
(
p
d
2
4
)
$\begin{array}{}
\displaystyle
(\sqrt[4]{pd^{2}})
\end{array}$
be a real pure quartic number field and k = ℚ(
p
$\begin{array}{}
\displaystyle
\sqrt{p}
\end{array}$
) its real quadratic subfield, where p ≡ 5 (mod 8) is a prime integer and d an odd square-free integer coprime to p. In this work, we calculate r
2(K), the 2-rank of the class group of K, in terms of the number of prime divisors of d that decompose or remain inert in ℚ(
p
$\begin{array}{}
\displaystyle
\sqrt{p}
\end{array}$
), then we will deduce forms of d satisfying r
2(K) = 2. In the last case, the 4-rank of the class group of K is given too.
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1 articles.
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