Geodesic
Unsolvability in radicals for a class of equations of degree five
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 163-164 
B. B. Lur'e; M. B. Gladkikh. Unsolvability in radicals for a class of equations of degree five. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 163-164. http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a10/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An easy sufficient condition for unsolvability in radicals of an irreducible equation of the fifth degree of the Bring–Jerard form defined over $\mathbb Z$ is found.

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

[2] B. B. Lure, “Kriterii nerazreshimosti v radikalakh nerazreshimogo uravneniya prostoi stepeni”, Tezisy dokladov Mezhdunarodnoi algebraicheskoi konferentsii pamyati Z. I. Borevicha, SPb., 2002, 46–47

[3] D. A. Grave, Elementy vysshei algebry, Kiev, 1914

[4] N. G. Chebotarev, Osnovy teorii Galua, ONTI, M.-L., 1936

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