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21.80 (2026)

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Do there exist finitely generated left-orderable groups with only one nontrivial conjugacy class?

A positive answer to this question implies a positive answer to 21.78. Note that D. Osin constructed torsion-free finitely generated groups with only one nontrivial conjugacy class; see 9.10.

Contributor: Y. Lodha, A. Navas

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