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16.51 (2006)

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Do there exist groups that can be right-ordered in infinitely countably many ways?

Contributor: V. M. Kopytov, N. Ya. Medvedev

Progress

There exist groups that can be fully ordered in infinitely countably many ways (R. Buttsworth).

*No, there are no such groups (A. Clay, Preprint, 2009, http://arxiv.org/abs/0909.0273; A. Navas, C. Rivas, Algebr. Geom. Topol., 9 (2009), 2079–2100, with an appendix by A. Clay; P. A. Linnell, Bull. London Math. Soc., 43 (2011), 200–202, based on (A. V. Zenkov, Sibirsk. Mat. Zh., 38 (1997), 90–92 (Russian), English transl., Siberian Math. J., 38, no. 1 (1997), 76–77), where this was proved for locally indicable groups.

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