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Exponential Genus Problems in One-Relator Products of Groups
 
A. J. Duncan University of Newcastle, Newcastle upon Tyne, England
Front Cover for Exponential Genus Problems in One-Relator Products of Groups
Available Formats:
Electronic ISBN: 978-1-4704-0477-2
Product Code: MEMO/186/873.E
156 pp 
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $43.20
Front Cover for Exponential Genus Problems in One-Relator Products of Groups
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  • Front Cover for Exponential Genus Problems in One-Relator Products of Groups
  • Back Cover for Exponential Genus Problems in One-Relator Products of Groups
Exponential Genus Problems in One-Relator Products of Groups
A. J. Duncan University of Newcastle, Newcastle upon Tyne, England
Available Formats:
Electronic ISBN:  978-1-4704-0477-2
Product Code:  MEMO/186/873.E
156 pp 
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $43.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1862007
    MSC: Primary 20; Secondary 57;

    Exponential equations in free groups were studied initially by Lyndon and Schützenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper the author shows that for finite systems of quadratic exponential equations decidability passes, under certain hypotheses, from the factor groups to free products and one-relator products.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Quadratic words
    • 3. Quadratic exponential equations and $\mathcal {L}$-genus
    • 4. Resolutions of quadratic equations
    • 5. Decision problems
    • 6. Pictures
    • 7. Corridors
    • 8. Angle assignment
    • 9. Curvature
    • 10. Configurations $C$
    • 11. Configurations $D$
    • 12. Final angle adjustment
    • 13. Isoperimetry
    • 14. Proof of Theorem 5.9
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Volume: 1862007
MSC: Primary 20; Secondary 57;

Exponential equations in free groups were studied initially by Lyndon and Schützenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper the author shows that for finite systems of quadratic exponential equations decidability passes, under certain hypotheses, from the factor groups to free products and one-relator products.

  • Chapters
  • 1. Introduction
  • 2. Quadratic words
  • 3. Quadratic exponential equations and $\mathcal {L}$-genus
  • 4. Resolutions of quadratic equations
  • 5. Decision problems
  • 6. Pictures
  • 7. Corridors
  • 8. Angle assignment
  • 9. Curvature
  • 10. Configurations $C$
  • 11. Configurations $D$
  • 12. Final angle adjustment
  • 13. Isoperimetry
  • 14. Proof of Theorem 5.9
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