ABSTRACT
If you replace 1 by I and –1 by X, the tables become identical; the only difference is in the names of the elements. This is an example of an isomorphism. Here are two more examples.
1 –1 1 1 –1
–1 –1 1
I X I I X X X I
0 1 2 3 0 0 1 2 3 1 1 2 3 0 2 2 3 0 1 3 3 0 1 2
1 i –1 –i 1 1 i –1
–1 –1-1
–i i i –i
–i –i-i
1 1 i
1 i –1
Here is an example where the two groups are not isomorphic.