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15.49 (2002)

Solved

A group $G$ is a unique product group if, for any finite nonempty subsets $X, Y$ of $G$, there is an element of $G$ which can be written in exactly one way in the form $xy$ with $x \in X$ and $y \in Y$. Does there exist a unique product group which is not left-orderable?

Contributor: P. Linnell

Progress

Yes, there does (N. Dunfield, Appendix B in S. Kionke, J. Raimbault, Doc. Math., 21 (2016), 873–915).

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