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6.22 (1978)

Solved

Construct a braid that belongs to the derived subgroup of the braid group but is not a commutator.

Contributor: G. S. Makanin

Progress

Let $x = \sigma_1, y = \sigma_2$ be the standard generators of the braid group $B_3$; then the braid $(xyxyx)^{12}(xy)^{-12}(xyx)^{-12}$ belongs to the derived subgroup of $B_3$ but is not a commutator (Yu. S. Semënov, Abstracts of the 10th All-Union Sympos. on Group Theory, Minsk, 1986, p. 207 (Russian)).

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