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10.12 (1986)

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Does there exist a finitely generated semigroup $S$ with cancellation having non-exponential growth and such that its group of left quotients $G = S^{-1}S$ (which exists) is a group of exponential growth? An affirmative answer would give a positive solution to Problem 12 in (S. Wagon, The Banach–Tarski Paradox, Cambridge Univ. Press, 1985).

Contributor: R. I. Grigorchuk

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