3
$\begingroup$

I am trying to understand Arnold's proof for the insolvability of the quintic from the manuscript:

https://web.williams.edu/Mathematics/lg5/394/ArnoldQuintic.pdf

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.

$\endgroup$
2

1 Answer 1

1
$\begingroup$

In Exercise 1, take $\alpha = 1/3$, say. That's a cube root, ie a single nested radical.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.