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.

如果对于每两个元素u，组G都具有Magnus属性。$v\in G$在具有相同法线闭合的情况下，u与v共轭或$v^{-\mathrm{1个}}$。O. Bogopolski和J. Howie独立证明了所有闭合可定向表面的基本基团均具有Magnus属性。O. Bogopolski和K. Sviridov证明了闭合的非定向表面的类似结果，但后来发现了一个案例。在本文中，我们将那些结果（可以视为自由组的Magnus扩展）概括为本地可指示组的Magnus扩展，并将添加组的影响视为直接因素。为此，我们还证明了适用于本地可指示组的Freiheitssatz版本，以及M. Edjvet将组添加为直接因子的结果。