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Commutators in Free Groups

Published online by Cambridge University Press:  20 November 2018

R. C. Lyndon  and
M. J. Wicks
R. C. Lyndon
Affiliation:
University of Michigan, Ann Arbor, Michigan 48109
M. J. Wicks
Affiliation:
University of Singapore, Singapore 1025
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We study the representations of an element of a free group as a commutator. For a given element g of a free group F, we are interested in the set of all pairs (x, y) of elements of F such that

(1)

where [x, y] = xyx-1 y-1. If g = 1, the problem is trivial. We assume henceforth that g ≠ 1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 101 - 106
Copyright
Copyright © Canadian Mathematical Society 1981

References

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