实纯四次数域K= π (pd24)的2秩

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-02-01 DOI:10.1216/rmj.2023.53.27

Mbarek Haynou, B. Sodaïgui, M. Taous

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引用次数: 0

摘要

。本文考虑了实纯四次数域K = Q (4 (cid:112) pd2)，其中p是素数，d是无平方正整数，使得d对p是素数。我们计算r 2 (K)为K的类群的2秩，并作为一个应用，我们展示了d的所有可能形式，其中K的2类群是平凡的(等价地:K的类数是奇数)，循环或同构于Z / 2n1z × Z / 2n2z，其中n i∈n∗。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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THE 2-RANK OF THE REAL PURE QUARTIC NUMBER FIELD K=ℚ(pd24)

. In this paper, we consider the real pure quartic number ﬁeld K = Q ( 4 (cid:112) pd 2 ) , where p is a prime number and d is a square-free positive integer such that d is prime to p . We compute r 2 ( K ) the 2 -rank of the class group of K and as an application we exhibit all possible forms of d for which the 2 -class group of K is trivial (equivalently: the class number of K is odd), cyclic or isomorphic to Z / 2 n 1 Z × Z / 2 n 2 Z , where n i ∈ N ∗ .

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来源期刊

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.