It is conjectured that an irreducible Artin group which is of infinite type has trivial center. The conjecture is known to be true for two-dimensional Artin groups and for a few other types of Artin groups. In this work, we show that the conjecture holds true for Artin groups which satisfy a condition stronger than being of infinite type. We use small cancellation theory of relative presentations.

中文翻译：

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关于 Artin 群中的一个猜想

推测无限型的不可约Artin群有平凡的中心。众所周知，该猜想对于二维 Artin 群和一些其他类型的 Artin 群是正确的。在这项工作中，我们表明该猜想适用于满足比无限类型更强的条件的 Artin 群。我们使用相对演示的小抵消理论。