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Preprint Number 1351

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1351. Yatir Halevi and Daniel Palacín
The dp-rank of abelian groups
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Submission date: 12 December 2017


An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally 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 the subgroup pA has infinite index for only finitely many primes.
Finally, it is shown that an infinite stable field of finite dp-rank is algebraically closed.

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Full text arXiv 1712.04503: pdf, ps.

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