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12.31 (1992)

Solved

For relatively free groups $G$, prove or disprove the following conjecture of P. Hall: if a word $v$ takes only finitely many values on $G$ then the verbal subgroup $vG$ is finite.

Contributor: S. V. Ivanov

Progress

The conjecture is disproved (A. Storozhev, Proc. Amer. Math. Soc., 124, no. 10 (1996), 2953–2954).

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