%0 Journal Article
%A Halevi, Yatir
%A Palacín Cruz, Daniel
%T The dp-rank of abelian groups
%D 2019
%@ 0022-4812
%@ 1943-5886
%U https://hdl.handle.net/20.500.14352/98555
%X An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there are only finitely many primes p such that the group A/pA is infinite and for every prime p, there are only finitely many natural numbers n such that (p^n A)[p]/(p^{n + 1} A)[p] is infinite. Finally, it is shown that an infinite stable field of finite dp-rank is algebraically closed.
%~