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Browsing Department of Computer Science by Subject "Algorithmic problems in groups"
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Item Novikov groups are right-orderable(2022) Lemieux, StephaneNovikov 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.