{
  "abstract": "In this paper, we calculate the unit groups and the $2$-class numbers of the fields $ \\mathbb{Q}(\\sqrt{2}, \\sqrt{q}, \\sqrt{rs})$, where $q\\equiv3\\pmod4$, $r$ and $s$ are distinct prime numbers satisfying some congruent conditions. As an application of our main results, we derive the precise 2-class number for each field in our family. Furthermore, we show that Greenberg's conjecture is verified for several infinite families of real biquadratic fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33110",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohamed Mahmoud Chems-Eddin"
    },
    {
      "name": "Hamza El Mamry"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxfd82f144y7g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33110",
  "fulltext_url": null,
  "id": "fxfd82f144y7g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33110",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223844105",
  "pdf_url": "https://arxiv.org/pdf/2610.33110",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxfd82f144y7g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33110",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33110"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the unit group of some triquadratic fields",
  "title_text": "On the unit group of some triquadratic fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/fxfd82f144y7g",
  "venue": "arXiv",
  "versions": []
}