Galois theory (intro)
General · Mathematics
Study notes
Q: Find Gal(ℚ(√2)/ℚ). What does it tell about x²-2? Automorphisms fixing ℚ: √2 → ±√2. {id, σ: σ(√2) = -√2}: order 2! |Gal| = 2 = [ℚ(√2):ℚ] ✓! σ swaps roots: symmetry of x²-2! (Solvable group ⟹ roots by radicals: √2 = ±√2!)