: The set of all these "valid" swaps forms a mathematical group, known as the Galois group of the polynomial.
This theorem establishes a bridge between two different mathematical worlds: Galois Theory Of Algebraic Equations 2nd Edition - MCHIP Galois' Theory Of Algebraic Equations
The fundamental insight is that the roots of a polynomial exhibit . : The set of all these "valid" swaps
: Galois theory looks at how you can swap (permute) the roots of an equation without changing the algebraic relations they satisfy. Galois' Theory Of Algebraic Equations