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- W72414314 abstract "We give a uniform construction that, on input of a recursive presentation $P$ of a group, outputs a recursive presentation of a torsion-free group, isomorphic to $P$ whenever $P$ is itself torsion-free. We use this to re-obtain a known result, the existence of a universal finitely presented torsion-free group; one into which all finitely presented torsion-free groups embed. We apply our techniques to show that recognising embeddability of finitely presented groups is $Pi^{0}_{2}$-hard, $Sigma^{0}_{2}$-hard, and lies in $Sigma^{0}_{3}$. We also show that the sets of orders of torsion elements of finitely presented groups are precisely the $Sigma^{0}_{2}$ sets which are closed under taking factors." @default.
- W72414314 created "2016-06-24" @default.
- W72414314 creator A5066614483 @default.
- W72414314 date "2011-07-07" @default.
- W72414314 modified "2023-09-27" @default.
- W72414314 title "The computational complexity of recognising embeddings in finitely presented groups" @default.
- W72414314 hasPublicationYear "2011" @default.
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