PSL(2,7) septimic fields with a power basis
Journal de Théorie des Nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 369-375.

Nous donnons un ensemble infini de corps de degré 7 monogènes distincts dont la clôture normale a pour groupe de Galois PSL(2,7).

We give an infinite set of distinct monogenic septimic fields whose normal closure has Galois group PSL(2,7).

Reçu le :
Publié le :
DOI : https://doi.org/10.5802/jtnb.801
Classification : 11R04,  11R32
Mots clés : Galois Group, Septimic Field, Power Basis
@article{JTNB_2012__24_2_369_0,
     author = {Melisa J. Lavallee and Blair K. Spearman and Qiduan Yang},
     title = {PSL$(2,7)$ septimic fields with a power basis},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {369--375},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {24},
     number = {2},
     year = {2012},
     doi = {10.5802/jtnb.801},
     zbl = {1280.11062},
     mrnumber = {2950697},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.801/}
}
TY  - JOUR
AU  - Melisa J. Lavallee
AU  - Blair K. Spearman
AU  - Qiduan Yang
TI  - PSL$(2,7)$ septimic fields with a power basis
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2012
DA  - 2012///
SP  - 369
EP  - 375
VL  - 24
IS  - 2
PB  - Société Arithmétique de Bordeaux
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.801/
UR  - https://zbmath.org/?q=an%3A1280.11062
UR  - https://www.ams.org/mathscinet-getitem?mr=2950697
UR  - https://doi.org/10.5802/jtnb.801
DO  - 10.5802/jtnb.801
LA  - en
ID  - JTNB_2012__24_2_369_0
ER  - 
Melisa J. Lavallee; Blair K. Spearman; Qiduan Yang. PSL$(2,7)$ septimic fields with a power basis. Journal de Théorie des Nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 369-375. doi : 10.5802/jtnb.801. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.801/

[1] H. Cohen, A Course in Computational Algebraic Number Theory. Springer-Verlag, 2000. | MR 1228206 | Zbl 0786.11071

[2] I. Gaál, Diophantine equations and power integral bases. New Computational Methods. Birkhauser, Boston, 2002. | MR 1896601 | Zbl 1016.11059

[3] M.-N. Gras, Non-monogénéité de l’anneau des entiers des extensions cycliques de Q de degré premier l5. J. Number Theory 23 (1986), 347–353. | MR 846964 | Zbl 0582.12003

[4] C. U. Jensen, A. Ledet, N. Yui, Generic Polynomials, constructive aspects of Galois theory, MSRI Publications. Cambridge University Press, 2002. | MR 1969648 | Zbl 1042.12001

[5] M. J. Lavallee, B. K. Spearman, K. S. Williams, and Q. Yang, Dihedral quintic fields with a power basis. Mathematical Journal of Okayama University, vol. 47 (2005), 75–79. | MR 2198862 | Zbl 1161.11393

[6] Y. Motoda, T. Nakahara and K. H Park, On power integral bases of the 2-elementary abelian extension fields. Trends in Mathematics, Information Center for Mathematical Sciences, Volume 8 (June 2006), Number 1, 55–63.

[7] M. Nair, Power free values of polynomials. Mathematika 23 (1976), 159–183. | MR 429801 | Zbl 0349.10039

[8] B. K. Spearman, A. Watanabe and K. S. Williams, PSL(2,5) sextic fields with a power basis. Kodai Math. J., Vol. 29 (2006), No. 1, 5–12. | MR 2222162 | Zbl 1096.11038

[9] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers. Third Edition, Springer, 2000. | MR 2078267 | Zbl 0717.11045

Cité par Sources :