Errata to ‘‘The construction of solvable polynomials”

Abstract

in order to include the case ν = 1. (When ν = 1, the argument of footnote 12 fails and no δ satisfies the requirements of the theorem. When the formula is stated as above, no δ is called for when ν = 1.) In the special case ν = 1, the definition of G(x) in (5.2) should be replaced by G(x) = x − sμ0 , where s0 is a nonzero Lagrange resolvent. (In this case, there is no m, but this G(x) has the μ needed roots αs0.) When ν = 1, the assertion to be proved in Section 7 reduces to a tautology. 2. Proposition 4.1 contains a serious error that does not affect the rest of the paper. The formula αsi → αsi+κ it gives for τ describes a permutation of the Lagrange resolvents, but does not describe an automorphism of Ω, so the proposition fails to provide the needed τ . (The τ constructed in the proof is an automorphism, but it does not combine with σ and η to generate the group.) Correction of the formula for τ implies corrections in the relations, but the main assertions remain: