# what does "product of two cyclic groups" mean

I am reading "Elliptic curve cryptosystems" and the link is here（https://www.ams.org/journals/mcom/1987-48-177/S0025-5718-1987-0866109-5/S0025-5718-1987-0866109-5.pdf）. I don't understand the meaning of "product of two cyclic groups" in it. Can anyone explain it to me? It's better to have a simple example.

It means that the group of points of $$E_K$$ is isomorphic to $$\mathbb{Z}_n \times \mathbb{Z}_m$$ (2-dimensional vectors). Addition of points on $$E_K$$ corresponds to addition of vectors. In other words, the group is generated by (at most) two points: there exists points $$P,Q$$ (generators) such that any point $$V$$ can be written as $$[a]P + [b]Q$$ for some integers $$a,b$$. Here, $$(a,b) \in \mathbb{Z}_n \times \mathbb{Z}_m$$ is the vector representation.