Sylow theorems
General · Mathematics
Study notes
Q: Show every group of order 15 is cyclic using Sylow. 15 = 3×5. n₅ ≡ 1 mod 5, n₅|3: n₅ = 1! n₃ ≡ 1 mod 3, n₃|5: n₃ = 1! Unique Sylow subgroups: both NORMAL! G ≅ ℤ₃ × ℤ₅ ≅ ℤ₁₅: CYCLIC! (Sylow forces structure!)