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12.10 (1992)

Solved

(P. Neumann). Can the free group on two generators be embedded in $\text{Sym}(\mathbb{N})$ so that the image of every non-identity element has only a finite number of orbits?

Contributor: A. M.W. Glass

Progress

Yes, it can (H. D. Macpherson, in: Ordered groups and infinite permutation groups, Partially based on Conf. Luminy, France, 1993 (Mathematics and its Applications, 354), Kluwer, Dordrecht, 1996, 221–230).

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