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

Fabienne Chouraqui

doi:10.1080/00927872.2021.1924766

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

Fabienne Chouraqui

Faculty of Natural Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let G be a group and H ₁,…,H_s 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
Pages (from-to)	4600-4615
Number of pages	16
Journal	Communications in Algebra
Volume	49
Issue number	11
DOIs	https://doi.org/10.1080/00927872.2021.1924766
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

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10.1080/00927872.2021.1924766

Cite this

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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