Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-06T04:53:23.655Z Has data issue: false hasContentIssue false
  • English
  • Français

Product of Two Commutators as a Square in a Free Group

Published online by Cambridge University Press:  20 November 2018

Jonell A. Comerford  and
Y. Lee
Jonell A. Comerford
Affiliation:
Department of Mathematics, Eastern Illinois University, Charleston, IL 61920
Y. Lee
Affiliation:
Department of Mathematics, University of Wisconsin-Parkside, Kenosha, WI 53141
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that, if [s,t][u, v] = x2 in a free group, x need not be a commutator. We arrive at our example by use of a result of D. Piollet which characterizes solutions of such equations using an algebraic interpretation of the mapping class group of the corresponding surface.

Keywords

20E0557M20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 190 - 196
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Birman, J. and Chillingworth, D., On the homeotopy group of a non-orientahle surface Proc. Camb. Phil. Soc. 71 (1972), 437–448.Google Scholar
2. Lyndon, R. C., Equations in groups. Bol. Soc. Bras. Mat., Vol. 11, No. 1 (1980), 79–102.Google Scholar
3. Piollet, D., Solutions dune equation quadratique dans le groupe libre. Discrete Mathematics 59 (1986), 115–123.Google Scholar
4. Wicks, M. J., Commutators in free products. J. London Math. Soc. 37 (1962), 433–444.Google Scholar