Condition for Solubility of Galois Group of Polynomial

Theorem

Let $P$ be a polynomial.

Let $G$ be the Galois group of $P$.

Then $G$ is soluble if and only if the roots of $P$ can be obtained from the coefficients of $P$ using just the arithmetic operations and raising to powers of the form $\dfrac 1 n$ for a natural number $n$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Galois theory
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Galois theory