Abstract
Let G be a group and H1,…,Hs be subgroups of G of indices respectively. In 1974, M. Herzog and J. Schönheim conjectured that if is a coset partition of G, then 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.
Acknowledgments
I am very grateful to the referee for his/her comments that improved very much the clarity and the readability of the article.