Complex Variables – Nonrepresentability by Radicals and Entire Functions

Question

It is known that an algebraic function with non-solvable monodromy group can not be represented by radicals. Where can we find a detailed proof about the nonrepresentability by radicals and entire (or meromorphic) functions of algebraic functions in some English references?

Answer 1

See e.g.:

• Vladimir Arnold: Collected Works. Springer

• Khovanskii, A.: Topological Galois Theory - Solvability and Unsolvability of Equations in Finite Terms. Springer 2014

• Khovanskii, A.: One dimensional topological Galois theory. 2019

• Askold Khovanskii - Publications

For the topological proofs without connection to representability in meromorphic functions, see e.g.: Is there an alternative proof of the Abel–Ruffini theorem?.