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11.74 (1990)

Solved

Let $G$ be a non-elementary hyperbolic group and let $G^n$ be the subgroup generated by the $n$-th powers of the elements of $G$.
$\qquad$ a) (M. Gromov). Is it true that $G/G^n$ is infinite for some $n = n(G)$?
$\qquad$ b) Is it true that $\bigcap_{n=1}^\infty G^n = \{1\}$?

Contributor: A. Yu. Olshanskii

Progress

a) Yes, it is; b) Yes, it is (S. V. Ivanov, A. Yu. Olshanskii, Trans. Amer. Math. Soc., 348, N 6 (1996), 2091–2138).

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