Torsion subgroup (reviewed)

The torsion subgroup of an abelian variety over a number field is the subgroup of elements of finite order; it is a finite group that is isomorphic to the direct sum of at most $2g$ cyclic groups, where $g$ is the dimension of the abelian variety.

The structure of the torsion subgroup can be compactly described by listing its sequence of elementary divisors $[d_1,\ldots,d_n]$, where each $d_i$ divides $d_{i+1}$, indicating a finite abelian group that is isomorphic to $\Z/d_1\Z\oplus \cdots \oplus\Z/d_n\Z$.