| 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 186; 2007; 156 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Quadratic words
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3. Quadratic exponential equations and $\mathcal {L}$-genus
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4. Resolutions of quadratic equations
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5. Decision problems
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6. Pictures
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7. Corridors
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8. Angle assignment
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9. Curvature
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10. Configurations $C$
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11. Configurations $D$
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12. Final angle adjustment
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13. Isoperimetry
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14. Proof of Theorem 5.9
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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 $D$
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12. Final angle adjustment
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13. Isoperimetry
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14. Proof of Theorem 5.9
