Sur la tour de Hilbert de certains corps
DOI:
https://doi.org/10.5269/bspm.v34i2.27471Resumen
In this paper, we determine the first Hilbert $2$-class field for some quartic cyclic number fields ${\mathrm k}$ and the Galois group of the second Hilbert $2$-class field of ${\mathrm k}$ over ${\mathrm k}$.
Referencias
1. A. Azizi, Unités de certains corps de nombres imaginaires et abéliens sur Q, Ann. Sci. Math. Québec, 23 (2), 15–21, (1999).
2. E. Brown and C. J. Parry, The 2-class group of certain biquadratic number fields II, Pacific Journal of Mathematics, 78 (1), 11–26, (1978).
3. D. Gorenstein, Finite groups, Harper and Row, New York, (1968).
4. M. N. Gras, Table numérique du nombre de classes et des unités des extensions cycliques réelles de degré 4 de Q, Publ. Math. Fac. Sciences de Besançon, Théorie des Nombres, 2, 1–79, (1977–78).
5. F. P. Heider and B. Schmithals, Zur Kapitulation der Idealklassen in unverzweigten primzyklischen Erweiterungen, J. Reine Angew. Math., 366, 1–25, (1982).
6. M. Ishida, The genus fields of algebraic number fields, Lecture notes in mathematics, 555, Springer-Verlag, London, (1976).
7. P. Kaplan, Divisibilité par 8 du nombre des classes des corps quadratiques dont le 2-groupe des classes est cyclique, et réciprocité biquadratique, J. Math. Soc. Japan, 25 (4), 596–608, (1973).
8. H. Kisilevsky, Number fields with class number congruent to 4 modulo 8 and Hilbert’s theorem 94, J. Number Theory, 8 (3), 271–279, (1976).
9. F. Lemmermeyer, Kuroda’s class number formula, Acta Arithmetica, 66 (3), 245–260, (1994).
10. F. Lemmermeyer, On 2-class field towers of imaginary quadratic number fields, J. de Théorie des Nombres de Bordeaux, 6 (2), 261–272, (1994).
11. L. C. Washington, Introduction to cyclotomic fields (Book 83), Graduate texts in mathematics, Springer–Verlag, New York, second edition, (1997).
2. E. Brown and C. J. Parry, The 2-class group of certain biquadratic number fields II, Pacific Journal of Mathematics, 78 (1), 11–26, (1978).
3. D. Gorenstein, Finite groups, Harper and Row, New York, (1968).
4. M. N. Gras, Table numérique du nombre de classes et des unités des extensions cycliques réelles de degré 4 de Q, Publ. Math. Fac. Sciences de Besançon, Théorie des Nombres, 2, 1–79, (1977–78).
5. F. P. Heider and B. Schmithals, Zur Kapitulation der Idealklassen in unverzweigten primzyklischen Erweiterungen, J. Reine Angew. Math., 366, 1–25, (1982).
6. M. Ishida, The genus fields of algebraic number fields, Lecture notes in mathematics, 555, Springer-Verlag, London, (1976).
7. P. Kaplan, Divisibilité par 8 du nombre des classes des corps quadratiques dont le 2-groupe des classes est cyclique, et réciprocité biquadratique, J. Math. Soc. Japan, 25 (4), 596–608, (1973).
8. H. Kisilevsky, Number fields with class number congruent to 4 modulo 8 and Hilbert’s theorem 94, J. Number Theory, 8 (3), 271–279, (1976).
9. F. Lemmermeyer, Kuroda’s class number formula, Acta Arithmetica, 66 (3), 245–260, (1994).
10. F. Lemmermeyer, On 2-class field towers of imaginary quadratic number fields, J. de Théorie des Nombres de Bordeaux, 6 (2), 261–272, (1994).
11. L. C. Washington, Introduction to cyclotomic fields (Book 83), Graduate texts in mathematics, Springer–Verlag, New York, second edition, (1997).
Descargas
Publicado
2015-06-29
Número
Sección
Research Articles
Licencia
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
