Generalising previous results on classical braid groups by Artin and Lin, we determine the values of m, n ∈ $\mathbb N$ for which there exists a surjection between the n- and m-string braid groups of an orientable surface without boundary. This result is essentially based on specific properties of their lower central series, and the proof is completely combinatorial. We provide similar but partial results in the case of orientable surfaces with boundary components and of non-orientable surfaces without boundary. We give also several results about the classification of different representations of surface braid groups in symmetric groups.

中文翻译：

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下中心系列、表面编织组、凸出和排列

概括 Artin 和 Lin 对经典编织组的先前结果，我们确定米,n∈$\mathbb N$之间存在一个凸出n- 和米- 无边界的可定向表面的弦编织组。这个结果本质上是基于它们下中心级数的特定性质，证明是完全组合的。在具有边界分量的可定向表面和没有边界的不可定向表面的情况下，我们提供了类似但部分结果。我们还给出了关于对称组中表面编织组的不同表示的分类的几个结果。