nLab
the Barsotti-Tate group of an abelian variety

Recall that a p-divisible group $G$ has the defining properties that $p{\mathrm{id}}_G:G\to G$ is an epimorphism with finite kernel satisfying $G={\cup }_j\ker p^j{\mathrm{id}}_G$.

Now let $A$ be any commutative algebraic $k$-group such that $p{\mathrm{id}}_A:A\to A$ is an epimorphism. Then

$$A(p):={\cup }_j\ker p^j{\mathrm{id}}_A$$A(p):=\cup_j ker \,p^j \,id_A

is a $p$-divisible group.