Geodesic
Commutators in Free Groups
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 101-106

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DOI

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. 
Lyndon, R. C.; Wicks, M. J. Commutators in Free Groups. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 101-106. doi: 10.4153/CMB-1981-016-1
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     title = {Commutators in {Free} {Groups}},
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