For equations of degree five or higher, the group of permutations is the alternating group Ancap A sub n
Arnold’s proof centers on how the roots of a polynomial behave as its coefficients move along closed loops in complex space: Abel's theorem in problems and solutions based ...
When coefficients traverse certain loops, the roots of the polynomial undergo a non-trivial permutation. For equations of degree five or higher, the
Theorem 1.2 (Abel's theorem) The general algebraic equation with one unknown of degree greater than 4 is insoluble in radicals, i. Stockholms universitet i. Stockholms universitet