Let $O := [0:1:0]$, and define addition on $E(\mathbb{F}_p)$ by the usual chord-and-tangent law with $O$ as the point at infinity. Then $E(\mathbb{F}_p)$ is a finite abelian group. Its identity element is $O$, and for every affine point $(x,y) \in E(\mathbb{F}_p)$ its inverse is