On singular equations over torsion-free groups

Martin Edjvet; James Howie

doi:10.1142/S0218196721500272

On singular equations over torsion-free groups

Martin Edjvet
, James Howie^*

^*Corresponding author for this work

School of Mathematical & Computer Sciences

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

3 Citations (Scopus)

Abstract

We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most 8. This result has applications to equations over torsion-free groups: in particular a singular equation of syllable length at most 18 over a torsion-free group has a solution in some overgroup.

Original language	English
Pages (from-to)	551-580
Number of pages	30
Journal	International Journal of Algebra and Computation
Volume	31
Issue number	3
Early online date	14 Apr 2021
DOIs	https://doi.org/10.1142/S0218196721500272
Publication status	Published - May 2021

Keywords

Equations over groups
One-relator products

ASJC Scopus subject areas

General Mathematics

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10.1142/S0218196721500272

Cite this

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title = "On singular equations over torsion-free groups",

abstract = "We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most 8. This result has applications to equations over torsion-free groups: in particular a singular equation of syllable length at most 18 over a torsion-free group has a solution in some overgroup.",

keywords = "Equations over groups, One-relator products",

author = "Martin Edjvet and James Howie",

note = "Funding Information: The second author was supported in part by Leverhulme Trust Emeritus Fellowship EM-2018-023\textbackslash{}9. Publisher Copyright: {\textcopyright} 2021 World Scientific Publishing Company.",

year = "2021",

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T1 - On singular equations over torsion-free groups

AU - Edjvet, Martin

AU - Howie, James

PY - 2021/5

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N2 - We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most 8. This result has applications to equations over torsion-free groups: in particular a singular equation of syllable length at most 18 over a torsion-free group has a solution in some overgroup.

AB - We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most 8. This result has applications to equations over torsion-free groups: in particular a singular equation of syllable length at most 18 over a torsion-free group has a solution in some overgroup.

KW - Equations over groups

KW - One-relator products

UR - https://www.scopus.com/pages/publications/85104569645

U2 - 10.1142/S0218196721500272

DO - 10.1142/S0218196721500272

M3 - Article

AN - SCOPUS:85104569645

SN - 0218-1967

VL - 31

SP - 551

EP - 580

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 3

ER -

On singular equations over torsion-free groups

Abstract

Keywords

ASJC Scopus subject areas

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