About an Extension of the Mirsky-Newman, Davenport-Rado Result to the Herzog-Schönheim Conjecture for Free Groups

Fabienne Chouraqui

doi:10.32037/agta-2021-015

About an Extension of the Mirsky-Newman, Davenport-Rado Result to the Herzog-Schönheim Conjecture for Free Groups

Fabienne Chouraqui

Department of Mathematics, Physics and Computer Science (Oranim Campus)

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

Abstract

Let G be a group and H₁,…, H_s be subgroups of G of indices d₁,…, d_s respectively. In 1974, M. Herzog and J. Schönheim conjectured that if {inline formula present}, α₁ ∈ G, is a coset partition of G, then d₁,…, d_s cannot be distinct. We consider the Herzog-Schönheim conjecture for free groups of finite rank and propose a new approach, based on an extension of the Mirsky-Newman, Davenport-Rado result for {inline formula preset}.

Original language	English
Pages (from-to)	107-122
Number of pages	16
Journal	Advances in Group Theory and Applications
Volume	12
DOIs	https://doi.org/10.32037/agta-2021-015
State	Published - Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 AGTA.

Keywords

Herzog-Schönheimconjecture
Schreier coset graph
free group

ASJC Scopus subject areas

Algebra and Number Theory

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10.32037/agta-2021-015

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title = "About an Extension of the Mirsky-Newman, Davenport-Rado Result to the Herzog-Sch{\"o}nheim Conjecture for Free Groups",

abstract = "Let G be a group and H1,…, Hs be subgroups of G of indices d1,…, ds respectively. In 1974, M. Herzog and J. Sch{\"o}nheim conjectured that if \{inline formula present\}, α1 ∈ G, is a coset partition of G, then d1,…, ds cannot be distinct. We consider the Herzog-Sch{\"o}nheim conjecture for free groups of finite rank and propose a new approach, based on an extension of the Mirsky-Newman, Davenport-Rado result for \{inline formula preset\}.",

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year = "2021",

month = dec,

doi = "10.32037/agta-2021-015",

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N2 - Let G be a group and H1,…, Hs be subgroups of G of indices d1,…, ds respectively. In 1974, M. Herzog and J. Schönheim conjectured that if {inline formula present}, α1 ∈ G, is a coset partition of G, then d1,…, ds cannot be distinct. We consider the Herzog-Schönheim conjecture for free groups of finite rank and propose a new approach, based on an extension of the Mirsky-Newman, Davenport-Rado result for {inline formula preset}.

AB - Let G be a group and H1,…, Hs be subgroups of G of indices d1,…, ds respectively. In 1974, M. Herzog and J. Schönheim conjectured that if {inline formula present}, α1 ∈ G, is a coset partition of G, then d1,…, ds cannot be distinct. We consider the Herzog-Schönheim conjecture for free groups of finite rank and propose a new approach, based on an extension of the Mirsky-Newman, Davenport-Rado result for {inline formula preset}.

KW - Herzog-Schönheimconjecture

KW - Schreier coset graph

KW - free group

UR - https://www.scopus.com/pages/publications/85129178200

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DO - 10.32037/agta-2021-015

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VL - 12

SP - 107

EP - 122

JO - Advances in Group Theory and Applications

JF - Advances in Group Theory and Applications

ER -

About an Extension of the Mirsky-Newman, Davenport-Rado Result to the Herzog-Schönheim Conjecture for Free Groups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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