Preview

Proceedings of the Institute of Mathematics of the NAS of Belarus

Advanced search

Unramified Galois extensions and subgroups of GLn

Abstract

We consider the natural action of Galois groups of unramified Galois extensions of number fields on finite Galois stable subgroups of $GL_n$.

About the Author

D. A. Malinin
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus

Minsk



References

1. Harbater D. Galois groups with prescribed ramification. Contemporary Math., 1994, vol. 174, pp. 35–60.

2. Ozaki Manabu. Construction of maximal unramified p-extensions with prescribed Galois groups. Invent math., 2011, vol. 183, pp. 649–680.

3. Bartels H.-J. Zur Galoiskohomologie definiter arithmetischer Gruppen. J. reine angew. Math., 1978, vol. 298, pp. 89–97.

4. Malinin D. A. Galois stability for integral representations of finite groups St. Petersburg Math. J., 2000, vol. 12, no. 3, pp. 106–145.

5. Malinin D. A. Integral representations of finite groups with Galois action. Dokl. Russ. Akad. Nauk, 1996, vol. 349, no. 3, pp. 303–305.

6. Ritter J.,Weiss A. Galois action on integral representations. J. London Math. Soc. (2), 1992, vol. 46, pp. 411–431.

7. Moret-Bailly L. Extensions de corps globaux a ramification et groupe de Galois donnes. C. R. Acad. Sci. Paris, Serie 1, 1990, vol. 311, pp. 273–276.

8. Maire Ch. On infinite unramified extensions. Pacific J. Math., 2000, vol. 192, no. 1, pp. 135–142.

9. Kondo T. Algebraic number fields with the discriminant equal to that of quadratic number field. J. Math. Soc. Japan, 1995, vol. 47, no. 1, pp. 31–36.

10. Yamamura K. Maximal unramified extensions of imaginary quadratic fields of small conductors. Journal de Theorie des Nombres de Bordeaux, 1997, vol. 9, pp. 405–448.

11. Pohst M. Berechnung kleiner Diskriminanten total reeller algebraischer Zahlko¨ rper. J. Reine angew. Math., 1975, vol. 278/279, pp. 278–300.

12. Bartels H.-J., Kitaoka Y. Endliche arithmetische Untergruppen der GLn. J. reine angew. Math., 1980, vol. 313, pp. 151–156.

13. Rohlfs J. Arithmetische definierte Gruppen mit Galois-operation. Invent. Math., 1978, vol. 48, pp. 185–205.

14. Malinin D. A. Integral representations of p-groups over local fields. Sov. Math. Dokl., 1990, vol. 40, no. 3, pp. 619–622.

15. Malinin D. A. Integral representations over local fields for p-groups of a given class of nilpotency. St. Petersburg Math. J., 1998, vol. 10, no. 1, pp. 58–67.

16. Ishkhanov V. V., Lur’e B. B., Faddeev D. K. The embedding problem in Galois theory. Moscow, Nauka, 1990.

17. Curtis C. W., Reiner I. Representation theory of finite groups and associative algebras. New York, Interscience, 1962.

18. Fröhlich A. Discriminants of algebraic number fields. Math Zeitschr., 1960, vol. 74, pp. 18–28.

19. Frobenius G. U¨ ber Beziehungen zwischen den Primidealen eines algebraischen Zahlko¨ rpers und den Substitutionen seiner Gruppe. Sitzber, Preussen Akad. Wiss., 1896, s. 689–705.

20. Chebotarev N. G. Foundations of Galois theory, Part II. Noordhoff, 1950 (in German).


Review

For citations:


Malinin D.A. Unramified Galois extensions and subgroups of GLn. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2025;33(1):20-27. (In Russ.)

Views: 15


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 1812-5093 (Print)