Isomorphisms

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.