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11.82 (1990)

Solved

Let $R$ be the normal closure of an element $r$ in a free group $F$ with the natural length function and suppose that $s$ is an element of minimal length in $R$. Is it true that $s$ is conjugate to one of the following elements: $r, r^{-1}, [r, f], [r^{-1}, f]$ for some $f \in F$?

Contributor: V. N. Remeslennikov

Progress

No, not always (J. McCool, Glasgow Math. J., 43, no. 1 (2001), 123–124).

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