局部可指示群的Magnus扩张
A Magnus extension for locally indicable groups
摘要：
一个群$G$具有Magnus性质，如果对于每两个具有相同正规闭包的元素$u$，$v \in G$，$u$与$v$或$v^{-1}$共轭。O. Bogopolski和J. Howie独立证明了所有闭可定向曲面的基本群都具有Magnus性质。对于闭的非可定向曲面，O. Bogopolski和K. Sviridov的案件，但提交人后来提到的一个案件除外。在这篇文章中，我们推广这些结果，可以被视为自由群的Magnus扩张，局部可指示群的Magnus扩张，并考虑添加一个群作为一个直接因素的影响。为了这个目的，我们还证明了局部可指示群的Freiheitsstrom的版本和M的结果。Edjvet添加一个组作为直接因素。
英文摘要：
A group $G$ possesses the Magnus property if for every two elements $u$, $v \in G$ with the same normal closure, $u$ is conjugate to $v$ or $v^{-1}$. O. Bogopolski and J. Howie proved independently that the fundamental groups of all closed orientable surfaces possess the Magnus property. The analogous result for closed non-orientable surfaces was proved by O. Bogopolski and K. Sviridov except for one case that was later covered by the author. In this article, we generalize those results, which can be viewed as Magnus extensions for free groups, to a Magnus extension for locally indicable groups and consider the influence of adding a group as a direct factor. For this purpose, we also prove versions of the Freiheitssatz for locally indicable groups and of a result by M. Edjvet adding a group as a direct factor.
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