The discussion confirms that the group II18 / <3> is not isomorphic to II3 due to a difference in the number of elements. II18 consists of 18 elements, while <3> contains 6 elements, resulting in II18 / <3> having 6 elements. In contrast, II3 contains only 3 elements. The conclusion is definitive: the groups cannot be isomorphic because isomorphism requires a one-to-one correspondence in the number of elements.
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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.aliciaislol said: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