This paper is dedicated to cabling on virtual braids. This construction gives a new generating set for the virtual pure braid group [Formula: see text]. We define simplicial group [Formula: see text] and its simplicial subgroup [Formula: see text] which is generated by [Formula: see text]. Consequently, we describe [Formula: see text] as HNN-extension and find presentation of [Formula: see text] and [Formula: see text]. As an application to classical braids, we find a new presentation of the Artin pure braid group [Formula: see text] in terms of the cabled generators.

中文翻译：

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虚拟布线及4股虚拟纯编织组结构

本文专门讨论虚拟编织层上的布线。这种构造为虚拟纯编织组提供了一个新的发电机组[公式：见正文]。我们定义单纯群[Formula: see text] 及其由[Formula: see text] 生成的单纯子群[Formula: see text]。因此，我们将 [Formula: see text] 描述为 HNN 扩展，并找到 [Formula: see text] 和 [Formula: see text] 的表示。作为对经典编织的应用，我们发现了 Artin 纯编织组 [公式：见正文] 的电缆发电机的新表示。