Primary torsion subgroup at a prime
= Primary torsion subgroup at a prime
{title2=$A\{p\}$}
= p-primary torsion
{c}
{synonym}
For an abelian group $A$, its $p$-primary torsion subgroup is $A\{p\}=\{a:p^ra=0\text{ for some }r\ge0\}$. It is zero exactly when $A[p]=0$, since a nonzero element of $p$-power order has a multiple of order $p$. Multiplication by an integer prime to $p$ is an automorphism on it.