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Proceedings of the American Mathematical Society

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On the conjugacy problem for $ F/R\sp{\prime} $


Author: C. K. Gupta
Journal: Proc. Amer. Math. Soc. 85 (1982), 149-153
MSC: Primary 20F10; Secondary 03D40, 20F05
DOI: https://doi.org/10.1090/S0002-9939-1982-0652430-X
MathSciNet review: 652430
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Abstract: Let $ F/R$ be a finitely generated recursively presented group with the solvable conjugacy problem and the solvable power problem. The conjugacy problem for $ F/R'$ when $ F/R$ is torsion free has been solved by Remeslennikov and Sokolov (Algebra and Logic 9 (1970), 342-349). In this note we prove that $ F/R'$ has the solvable conjugacy problem even when $ F/R$ is not torsion free. This allows us, in particular, to conclude the solvability of the conjugacy problem for $ F/[{F^n},{F^n}]$ in terms of the conjugacy problem for $ F/{F^n}$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0652430-X
Article copyright: © Copyright 1982 American Mathematical Society