Novikov groups are right-orderable
Algorithmic problems in groups, conjugacy problem, right-orderable groups, word problem
Novikov groups were introduced as examples of finitely presented groups with unsolvable conjugacy problem. It was Bokut who showed that each Novikov group has a standard basis and thus a solvable word problem. Further, he showed that for every recursively enumerable degree of unsolvability d there is a Novikov group whose conjugacy problem is of degree d. In the present work, we show that Novikov groups are also right-orderable, thus exhibiting the first known examples of finitely presented right-orderable groups with solvable word problem and unsolvable conjugacy problem.
Lemieux, S. (2022) Novikov groups are right-orderable. Communications in Algebra, 50:8, 3354-3363. https://doi.org/10.1080/00927872.2022.2032119
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