How to show that the groups \$(Z_4, +_4)\$ and \$(Z_5, ・_5)\$ are isomorphic? [on hold]

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?