Abstract Let G be a group and H 1,…,Hs be subgroups of G of indices respectively. In 1974, M. Herzog and J. Schönheim conjectured that if is a coset partition… Click to show full abstract
Abstract Let G be a group and H 1,…,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.
               
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