Franz Lemmermeyer

Thesis

My Ph.D. thesis "Die Konstruktion von Klassenkörpern" (1994) on the explicit construction of Hilbert 2-class fields has remained more or less unpublished. On this page I will collect an English translation of this thesis with minor corrections.
  1. Preface
  2. Introduction
  3. Genus and Central Class Fields
  4. Separants
  5. Cyclic Extensions
  6. Cyclic Extensions: Ramification at infinite primes
  7. Dihedral Extensions
  8. Quaternion Extensions
  9. Artin-Furtwängler Extensions
  10. The Remaining Non-abelian Groups of Order 16
  11. Galois Groups of the Second Hilbert Class Field
  12. Tate's Example
  13. Base Fields of Higher Degree
  14. Explicit 2-Class Field Towers
  15. Tables
  16. Bibliography