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?



Nonrepresentability by radicals and entire (or meromorphic) functions of algebraic functions
See e.g.:


* Vladimir Arnold: Collected Works. Springer
* [Khovanskii, A.: Topological Galois Theory - Solvability and Unsolvability of Equations in Finite Terms. Springer 2014](https://doi.org/10.1007/978-3-642-38871-2)
* [Khovanskii, A.: One dimensional topological Galois theory. 2019](https://arxiv.org/abs/1904.03341)
* [Askold Khovanskii - Publications](https://www.math.toronto.edu/askold/)


For the topological proofs without connection to representability in meromorphic functions, see e.g.: [Is there an alternative proof of the Abel–Ruffini theorem?](https://math.stackexchange.com/questions/1550990/is-there-an-alternative-proof-of-the-abel-ruffini-theorem).


