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arXiv 1107.1489math.GRmath.LO
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关于群的挠

On torsion in finitely presented groups

Maurice Chiodo

备注：
11 pages. This is the version submitted for publication
发表信息：
On torsion in finitely presented groups, Groups Complex. Cryptol. 6 (2014), no. 1, 1-8
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摘要：

我们给出了一个统一的结构，输入的递归表示$P$的一组，输出的递归表示的无扭群，同构于$P$每当$P$本身是无扭的。我们用这个重新获得一个已知的结果，存在一个普遍的无挠群，所有的无挠群嵌入其中。我们应用我们的技术表明，识别嵌入性的非线性呈现的群体是$Π^{0}_{2}$ -硬，$Σ^{0}_{2}$ -硬，并在于$Σ^{0}_{3}$。我们还证明了群的扭元的阶集恰是在取因子下闭的$Σ^{0}_{2}$集。

英文摘要：

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 $Π^{0}_{2}$-hard, $Σ^{0}_{2}$-hard, and lies in $Σ^{0}_{3}$. We also show that the sets of orders of torsion elements of finitely presented groups are precisely the $Σ^{0}_{2}$ sets which are closed under taking factors.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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