Geodesic
Cyclic Galois extensions for quintic equation
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 78-90 
K. Y. Gudkov; B. B. Lur'e. Cyclic Galois extensions for quintic equation. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 78-90. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a6/
@article{ZNSL_2016_443_a6,
     author = {K. Y. Gudkov and B. B. Lur'e},
     title = {Cyclic {Galois} extensions for quintic equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {78--90},
     year = {2016},
     volume = {443},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a6/}
}
TY  - JOUR
AU  - K. Y. Gudkov
AU  - B. B. Lur'e
TI  - Cyclic Galois extensions for quintic equation
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 78
EP  - 90
VL  - 443
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a6/
LA  - ru
ID  - ZNSL_2016_443_a6
ER  - 
%0 Journal Article
%A K. Y. Gudkov
%A B. B. Lur'e
%T Cyclic Galois extensions for quintic equation
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 78-90
%V 443
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a6/
%G ru
%F ZNSL_2016_443_a6

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The authors investigate cyclic Galois extensions for quintic equation, and construct resolvent for real fields and fields, containing square root of $-1$. Also they prove a theorem that characterizes all Galois extensions for quintics.

[1] M. M. Postnikov, Teoriya Galua, Fizmatgiz, 1963

[2] F. Klein, Lektsii ob ikosaedre i reshenii uravnenii pyatoi stepeni, Per. s nem., ed. A. N. Tyurin, Nauka. Gl. red. fiz.-mat. lit., 1989 | MR

[3] N. G. Chebotarev, Osnovy teorii Galua, Gos. tekhn.-teor. izd-vo, 1934

[4] David A. Cox, Galois theory, 2nd edition, A John Wiley Sons, inc., 2012 | MR | Zbl

[5] C. Jensen, N. Yui, “Polynomials with $D_p$ as Galois group”, J. Number Theory, 15 (1982), 347–375 | DOI | MR | Zbl

[6] C. Williamson, “Odd degree polynomials with dihedral Galois groups”, J. Number Theory, 34 (1990), 153–173 | DOI | MR | Zbl

[7] E. Galua, Matematicheskie raboty, Institut kompyuternykh issledovanii, 2002

[8] B. Spearman, K. Williams, “Dihedral quintic polynomials and a theorem of Galois”, Indian J. Pure Appl. Math., 30:9 (1999), 839–845 | MR | Zbl

[9] B. Lure, “Kriterii nerazreshimosti v radikalakh uravnenii prostoi stepeni”, Dokl. RAN, 388 (2003), 447–448 | MR | Zbl