Direct products of groups
General · Mathematics
Study notes
Q: Show ℤ₂ × ℤ₃ ≅ ℤ₆. Is ℤ₂ × ℤ₂ cyclic? (1,1): order lcm(2,3) = 6: generates all 6: CYCLIC ≅ ℤ₆! ℤ₂×ℤ₂: every non-identity has order 2: max order 2 < 4: NOT cyclic! ≅ Klein V₄! (Coprime orders: product cyclic!)