Geodesic
On Commutator Equalities and Stabilizersin Free Groups
Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 263-267

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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), (a 2, 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. 
Burns, R. G.; Edmunds, C. C.; Farouqi, I. H. On Commutator Equalities and Stabilizersin Free Groups. Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 263-267. doi: 10.4153/CMB-1976-041-7
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     title = {On {Commutator} {Equalities} and {Stabilizersin} {Free} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {263--267},
     year = {1976},
     volume = {19},
     number = {3},
     doi = {10.4153/CMB-1976-041-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-041-7/}
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