Abstract
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 language | English |
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Pages (from-to) | 4600-4615 |
Number of pages | 16 |
Journal | Communications in Algebra |
Volume | 49 |
Issue number | 11 |
DOIs | |
State | Published - 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.
Keywords
- free groups
- Herzog-Schonheim conjecture
- Schreier coset graphs
ASJC Scopus subject areas
- Algebra and Number Theory