I am doing CLRS exercise 31.3-1.

The question is to show that these groups $ (Z_4, +_4)$ and $ (Z_5, ・_5)$ are isomorphic by exhibiting a one-to-one correspondance α between their elements such that $ a + b ≡ c $ (mod 4) if and only if $ α(a)・α(b)≡α(c)$ (mod 5).

I understand that we have the following tables:

$ (Z_4, +_4)$

` 0 1 2 3 0 0 1 2 3 1 1 2 3 4 2 2 3 0 1 3 3 0 1 2 `

$ (Z_5, ・_5)$

` 1 2 3 4 1 1 2 3 4 2 2 4 1 3 3 3 1 4 2 4 4 3 2 1 `

But what does it mean to find isomorphic relationships between these two tables?