Herzog–Schönheim conjecture, vanishing sums of roots of Unity and convex polygons

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Let G be a group and H 1,…,Hs be subgroups of G of indices (Formula presented.) respectively. In 1974, M. Herzog and J. Schönheim conjectured that if (Formula presented.) is a coset partition of G, then (Formula presented.) cannot be pairwise distinct. In this article, we present the conjecture as a problem on vanishing sum of roots of unity and convex polygons and prove some results using this approach.

Original languageEnglish
Pages (from-to)4600-4615
Number of pages16
JournalCommunications in Algebra
Issue number11
StatePublished - 2021

Bibliographical note

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© 2021 Taylor & Francis Group, LLC.


  • Herzog-Schonheim conjecture
  • Schreier coset graphs
  • free groups

ASJC Scopus subject areas

  • Algebra and Number Theory


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