Minimal additive complements in finitely generated abelian groups

Arindam Biswas, Jyoti Prakash Saha

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Given two nonempty subsets W, W⊆ G in an arbitrary abelian group G, the set W is said to be an additive complement to W if W+ W= G and it is minimal if no proper subset of W is a complement to W. The notion was introduced by Nathanson and previous works by him, Chen–Yang, Kiss–Sándor–Yang, etc. focussed on G= Z. In this article, we focus on the higher rank case. We introduce the notion of “spiked subsets” and give necessary and sufficient conditions for the existence of minimal complements for them. This provides an answer to a problem of Nathanson in several contexts.

Original languageEnglish
Pages (from-to)215-238
Number of pages24
JournalRamanujan Journal
Issue number1
StatePublished - 1 Jan 2022
Externally publishedYes


  • Additive complements
  • Additive number theory
  • Minimal complements
  • Sumsets

ASJC Scopus subject areas

  • Algebra and Number Theory


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