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Powers of Genus two in Free Groups

Published online by Cambridge University Press:  20 November 2018

Charles C. Edmunds  and
Gerhard Rosenberger
Charles C. Edmunds
Affiliation:
Department of Mathematics Mount Saint Vincent University Halifax, Nova Scotia Canada B3M 2J6
Gerhard Rosenberger
Affiliation:
Fachbereich Mathematik Universität Dortmund Postfach 50 05 00 4600 Dortmund 50 Fed. Rep. of Germany
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Abstract

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The general problem is to express an element of the derived group of a free group as a product of a minimal number of commutators. An old conjecture is settled in the negative, and a new conjecture and a number of related questions are posed.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 342 - 344
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Comerford, J. and Lee, Y., Product of two commutators as a square in a free group, Canad. Math. Bull., 33 (1990), 190–196.Google Scholar
2. Culler, M., Using surfaces to solve equations if free groups, Topology 20 (1981), 133–267.Google Scholar
3. Edmunds, C. C., A short combinatorial proof of the Vaught conjecture, Canad. Math. Bull. 18 (1975), 607–608.Google Scholar
4. Lyndon, R. C., The equation a2b2 = c2 in free groups, Michigan Math. J. 6 (1959), 89–95.Google Scholar
5. Lyndon, R. C., Equations in groups, Bol. Soc. Bras. Mat. 11 (1980), 79–102.Google Scholar
6. Massey, W. S., Algebraic Topology: An Introduction, Springer-Verlag, New York, (1977).Google Scholar
7. Rosenberger, G., Minimal generating systems for plane discontinuous groups and an equation in free groups, Proc. of “Groups-Korea 1988”, (to appear).Google Scholar
8. Schützenberger, M. P., Sur l'équation a 2+nb2+m = c2+p dans un group libre, C. R. Acad. Sci. Paris 248 (1959), 2435–2436.Google Scholar
9. Wicks, M. J., Commutators in free products, J. London Math. Soc. 37 (1962), 433–444.Google Scholar