On a conjecture of Lemmermeyer,International Journal of Number Theory

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On a conjecture of Lemmermeyer
International Journal of Number Theory ( IF 0.5 ) Pub Date : 2020-02-20 , DOI: 10.1142/s1793042120500748
Siham Aouissi ₁ , Mohamed Talbi ₂ , Moulay Chrif Ismaili ₁ , Abdelmalek Azizi ₁

Affiliation

Let [Formula: see text] be a prime and denote by [Formula: see text] a primitive third root of unity. Recently, Lemmermeyer presented a conjecture about [Formula: see text]-class groups of pure cubic fields [Formula: see text] and of their normal closures [Formula: see text]. The main goal of this paper is to reduce Lemmermeyer’s conjecture to a problem of unit theory by showing that the conjecture of Lemmermeyer follows from Conjecture 2.9.

中文翻译：

关于 Lemmermeyer 的猜想

令 [Formula: see text] 为质数，并由 [Formula: see text] 表示原始的第三个单位根。最近，Lemmermeyer 提出了一个关于 [Formula: see text] 类群的纯三次域 [Formula: see text] 及其正常闭包 [Formula: see text] 的猜想。本文的主要目的是通过证明 Lemmermeyer 的猜想源自猜想 2.9，将 Lemmermeyer 猜想简化为单位论问题。

更新日期：2020-02-20

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