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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
List Price: $72.00 MAA Member Price:$64.80
AMS Member Price: $43.20 Click above image for expanded view 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  List Price:$72.00 MAA Member Price: $64.80 AMS Member Price:$43.20
• Book Details

Memoirs of the American Mathematical Society
Volume: 1862007; 156 pp
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
• 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 $D$
• 13. Isoperimetry
• 14. Proof of Theorem 5.9
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Volume: 1862007; 156 pp
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
• 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 $D$