Geodesic
Products of Commutators as Products of Squares
Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1329-1335

Voir la notice de l'article provenant de la source Cambridge University Press

In any group G, the commutator subgroup G' is contained in G2, the subgroup of G generated by the squares in G. Thus any product of commutators can be written as a product of squares in G. For instance, the commutator [x, y] ( = xyx-1y-1 ) can be expressed as the product of three squares: [x, y] = x 2(x -1 y)2(y -1)2. Roger Lyndon and Morris Newman have made the interesting observation [4, Theorem 1] that, in this case, the number three is minimal in the sense that there are groups which contain commutators not expressible as the product of fewer than three squares. 
Edmunds, Charles C. Products of Commutators as Products of Squares. Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1329-1335. doi: 10.4153/CJM-1975-135-6
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