On 2-ciass field towers of some imaginary quadratic number fields

  • F. Lemmermeyer


We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2, 2, 2) whose Hilbert 2-class fields are finite.


Prime Ideal Unit Group Galois Group Class Number Ideal Class 
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  1. [1]
    E. Benjamin, F. Lemmermeyer and C. Snyder,Real Quadratic Fields with Abelian 2-Class Field Tower, submitted.Google Scholar
  2. [2]
    E. Benjamin, F. Sanborn andC. Snyder,Capitulation in Unramified Quadratic Extensions of Real Quadratic Number Fields, Glasgow Math. J.36 (1994), 385–392.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    O. Grün,Aufgabe 153; Lösungen von L. Holzer und A. Scholz, Jahresber. DMV45 (1934), 74–75.Google Scholar
  4. [4]
    F. Hajir,On a theorem of Koch, Pac. J. Math.176 (1996), 15-18.Google Scholar
  5. [5]
    H. Hasse,Zahlbericht. Teil II, Würzburg-Wien 1970.Google Scholar
  6. [6]
    F. Lemmermeyer,Kuroda’s Class Number Formula, Acta Arith.66.3 (1994), 245–260.MathSciNetGoogle Scholar
  7. [7]
    —,Ideal class groups of cyclotomic number fields I, Acta Arith.72 (1995), 347–359.MATHMathSciNetGoogle Scholar
  8. [8]
    —,Unramified quaternion extensions of quadratic number fields, J. Théor. Nombres Bordeaux9 (1997), 51–88.MATHMathSciNetGoogle Scholar
  9. [9]
    J. Martinet,Petits discriminants des corps de nombres, Journées Arithmétiques 1980 (J. V. Armitage, ed.), Cambridge Univ. Press 1982, 151-193.Google Scholar
  10. [10]
    G. Poitou,Minorations de discriminants, Sém. Bourbaki (1975/76)479 (1977), 136–153.MathSciNetGoogle Scholar
  11. [11]
    H. Richter,Über die Lösbarkeit einiger nicht-Abelscher Einbettungsprobleme, Math. Annalen112 (1936), 69–84.CrossRefGoogle Scholar
  12. [12]
    scR. Schoof,Letter from Nov. 13, 1992.Google Scholar
  13. [13]
    K. Yamamura,Maximal unramified extensions of imaginary quadratic number fields of small conductors, preprint 1996.Google Scholar

Copyright information

© Mathematische Seminar 1997

Authors and Affiliations

  1. 1.Universität des SaarlandesD-66041 Saarbrücken

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