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On Commutator Equalities and Stabilizersin Free Groups

Published online by Cambridge University Press:  20 November 2018

R. G. Burns
Affiliation:
York University, Toronto
C. C. Edmunds
Affiliation:
Mount Saint Vincent University, Halifax
I. H. Farouqi
Affiliation:
University of Karachi, Karachi
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Abstract

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A simple proof is given of a result of Hmelevskiï on the solutions of the equation [x, y] = [u, υ] over a free group for any specified u, υ. To illustrate, the equation is solved explicitly for (u, υ) = (a, b), (a2, b), ([a, b], c) (where a, b, c freely generate the free group) and thence stabilizers of the corresponding commutators in the automorphism group of this free group are determined.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1976

References

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