Novikov groups are right-orderable

Lemieux, Stephane

Novikov groups are right-orderable

Author

Lemieux, Stephane

Date

2022

Keywords

Algorithmic problems in groups, conjugacy problem, right-orderable groups, word problem

Abstract (summary)

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.