Divisibility by a prime
= Divisibility by a prime
{title2=$pA=A$}
= p-divisibility
{c}
{synonym}
An abelian group $A$ is $p$-divisible when multiplication by $p$ is surjective, equivalently $A/pA=0$. This does not mean it has no $p$-torsion: $\mathbb Q/\mathbb Z$ is divisible and has elements of every finite order. The <Kummer cohomology divisibility criterion> relates this property to <Galois cohomology>.