Arnold’s proof centers on how the roots of a polynomial behave as its coefficients move along closed loops in complex space:
If a root were representable by radicals, its corresponding "monodromy group" would have to be solvable. Abel's theorem in problems and solutions based ...
When coefficients traverse certain loops, the roots of the polynomial undergo a non-trivial permutation. Arnold’s proof centers on how the roots of
The primary objective of this work is to present a of Abel's Impossibility Theorem. This theorem states that there is no general formula for the roots of a polynomial equation of degree five or higher using only arithmetic operations and radicals. i. Stockholms universitet
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