I am trying to understand Arnold's proof for the insolvability of the quintic from the manuscript:
which is actually well written. However, I am stumbling in Page 4 where the author says "By contrast, Exercise 1 implies that any combination of the four field operations, continuous functions, and a single nesting of radicals would produce a loop." and the subsequent Proposition 6.
Where does the single nesting of radicals come in Exercise 1? There is no nesting of radicals mentioned before this statement. Can anyone help? Thanks.