Q: What is the Galois group of a polynomial? A: The Galois group of a polynomial is the group of automorphisms of its splitting field that fix the base field.
Let $f(x) = x^3 - 2 \in \mathbb{Q}[x]$. Compute the Galois group of $f(x)$ over $\mathbb{Q}$. Dummit And Foote Solutions Chapter 14
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Let $K$ be a field and let $f(x) \in K[x]$ be a separable polynomial. Show that the Galois group of $f(x)$ over $K$ acts transitively on the roots of $f(x)$. Q: What is the Galois group of a polynomial
Q: What is Galois Theory? A: Galois Theory is a branch of Abstract Algebra that studies the symmetry of algebraic equations. Dummit And Foote Solutions Chapter 14
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