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.
Bibliographical noteFunding Information:
I am very grateful to the referee for his/her comments that improved very much the clarity and the readability of the article.
© 2021 Taylor & Francis Group, LLC.
- free groups
- Herzog-Schonheim conjecture
- Schreier coset graphs
ASJC Scopus subject areas
- Algebra and Number Theory