Using EDT0L systems to solve some equations in the solvable Baumslag-Solitar groups

Andrew   Duncan; Alex Evetts; Derek F.   Holt; Sarah   Rees

doi:10.1016/j.jalgebra.2023.04.020

Using EDT0L systems to solve some equations in the solvable Baumslag-Solitar groups

Andrew Duncan, Alex Evetts, Derek F. Holt, Sarah Rees

Pure Mathematics

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

Abstract

We investigate the solution sets to equations in the solvable Baumslag-Solitar groups BS(1, k), k ≥ 2, and show that these sets are represented by edt0l languages in some cases. In particular, we prove that the multiplication table of such a group forms an edt0l language with respect to a specific natural normal form for group elements.

Original language	English
Pages (from-to)	434-456
Number of pages	22
Journal	Journal of Algebra
Volume	630
Early online date	2 May 2023
DOIs	https://doi.org/10.1016/j.jalgebra.2023.04.020
Publication status	Published - 15 Sept 2023

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title = "Using EDT0L systems to solve some equations in the solvable Baumslag-Solitar groups",

abstract = "We investigate the solution sets to equations in the solvable Baumslag-Solitar groups BS(1, k), k ≥ 2, and show that these sets are represented by edt0l languages in some cases. In particular, we prove that the multiplication table of such a group forms an edt0l language with respect to a specific natural normal form for group elements.",

author = "Andrew Duncan and Alex Evetts and Holt, {Derek F.} and Sarah Rees",

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AU - Duncan, Andrew

AU - Evetts, Alex

AU - Holt, Derek F.

AU - Rees, Sarah

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N2 - We investigate the solution sets to equations in the solvable Baumslag-Solitar groups BS(1, k), k ≥ 2, and show that these sets are represented by edt0l languages in some cases. In particular, we prove that the multiplication table of such a group forms an edt0l language with respect to a specific natural normal form for group elements.

AB - We investigate the solution sets to equations in the solvable Baumslag-Solitar groups BS(1, k), k ≥ 2, and show that these sets are represented by edt0l languages in some cases. In particular, we prove that the multiplication table of such a group forms an edt0l language with respect to a specific natural normal form for group elements.

U2 - 10.1016/j.jalgebra.2023.04.020

DO - 10.1016/j.jalgebra.2023.04.020

M3 - Article

SN - 0021-8693

VL - 630

SP - 434

EP - 456

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Using EDT0L systems to solve some equations in the solvable Baumslag-Solitar groups

Abstract

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