Isomorphism between II18 / <3> and II3

[aliciaislol]

Homework Statement

Show that II₁₈ / <3> is isomorphic to II₃.

Homework Equations

II₁₈ = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}
<3> = {0,3,6,9,12,15}
II₃ = {1,2,3}
II₁₈ / <3> = {3,6,9,12,15,18}

The Attempt at a Solution

 

[HallsofIvy]

Homework Statement

Show that II₁₈ / <3> is isomorphic to II₃.

Homework Equations

II₁₈ = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}
<3> = {0,3,6,9,12,15}
II₃ = {1,2,3}
II₁₈ / <3> = {3,6,9,12,15,18}

The Attempt at a Solution

Looks to me like your proof says they are NOT isomorphic! If they don't have the same number of members, they certainly aren't isomorphic.