On the unit group and the 2-class number of ℚ(√(2),√(p),√(q))

2024/03/17 by Mohamed Mahmoud Chems-Eddin, Chems-Eddin, Mohamed Mahmoud, Moha Ben Taleb El Hamam +3 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2403.17972

openalex publication_date 2024/03/17 · openalex created_date 2024/03/29 · openalex updated_date 2026/07/28

Abstract

Let p≡ 1\pmod8 and q≡7\pmod 8 be two prime numbers. The purpose of this paper is to compute the unit group of the fields \KK=\QQ(√ 2, √(p), √(q) ) and give their 2-class numbers.

Cited by

• Greenberg's conjecture and Inverse Galois problem: metacyclic-nonmodular group of type 1 whose abelianization is ℤ/2 ℤ×ℤ/2^m ℤ, m≥ 2
• The unit group and the 2-class number of some fields of the form ℚ(√(2), √(pq), √(ps)) and ℚ(√(2), √(pq), √(ps), √(-ℓ))

Related

• On the unit group of some multiquadratic fields
• The unit group and the 2-class number of some fields of the form ℚ(√(2), √(pq), √(ps)) and ℚ(√(2), √(pq), √(ps), √(-ℓ))
• Arithmetic of some real triquadratic fields; Units and 2-class groups
• On the rank of the 2-class group of ℚ(√(p), √(q),√(-1))
• On Class Numbers of Pure Quartic fields