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

Research output: Contribution to journalArticlepeer-review


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

Funding Information:
I am very grateful to the referee for his/her comments that improved very much the clarity and the readability of the article.

Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.


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

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Herzog–Schönheim conjecture, vanishing sums of roots of Unity and convex polygons'. Together they form a unique fingerprint.

Cite this