Normal subgroups and quotient groups
General · Mathematics
Study notes
Q: Is H = {e,(12)} normal in S₃? Form ℤ₆/⟨3⟩. (13)H = {(13),(13)(12)} = {(13),(132)}. H(13) = {(13),(12)(13)} = {(13),(123)}: DIFFER: not normal! ℤ₆/⟨3⟩: cosets {0,3},{1,4},{2,5}: order 3: ≅ ℤ₃! (1+H)+(1+H) = 2+H ✓!