论文标题
局部指示组的马格努斯扩展
A Magnus extension for locally indicable groups
论文作者
论文摘要
如果每两个元素$ u $，$ v \ in g $，则具有同一正常闭合，$ u $与$ v $或$ v $或$ v^{ - 1} $相连，则组$ g $具有Magnus属性。 O. Bogopolski和J. Howie独立地证明了所有可定向的表面的基本群体具有Magnus属性。 O. Bogopolski和K. Sviridov证明了封闭不可取向表面的类似结果，除了后来作者涵盖的一个案例。在本文中，我们概括了这些结果，可以将这些结果视为自由组的马格努斯扩展，以作为本地指示组的Magnus扩展名，并考虑将添加组添加为直接因素的影响。为此，我们还证明了Freiheitssatz的局部指示组的版本，以及M. Edjvet的结果，将组添加为直接因素。
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.
