Geodesic
Product of Two Commutators as a Square in a Free Group
Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 190-196

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DOI

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.
DOI : 10.4153/CMB-1990-032-4
Mots-clés : 20E05, 57M20 
Comerford, Jonell A.; Lee, Y. Product of Two Commutators as a Square in a Free Group. Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 190-196. doi: 10.4153/CMB-1990-032-4
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     title = {Product of {Two} {Commutators} as a {Square} in a {Free} {Group}},
     journal = {Canadian mathematical bulletin},
     pages = {190--196},
     year = {1990},
     volume = {33},
     number = {2},
     doi = {10.4153/CMB-1990-032-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-032-4/}
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