G.N. Chebotarev's "On the Problem of Resolvents"

Abstract

This is an English translation of G.N. Chebotarev's classical paper "On the Problem of Resolvents," which was originally written in Russian and published in Vol. 114, No. 2 of the Scientific Proceedings of the V.I. Ulyanov-Lenin Kazan State University. In this paper, Chebotarev extends the method in Wiman's "On the Application of Tschirnhaus Transformations to the Reduction of Algebraic Equations" to argue that the general polynomial of degree 21 admits a solution using algebraic functions of at most 15 variables. However, his and Wiman's proofs assume that certain intersections in affine space are generic without proof.