Abstract Given a group action on a finite-dimensional CAT ⁢ ( 0 ) {\mathrm{CAT}(0)} cube complex, we give a simple criterion phrased purely in terms of cube stabilisers that ensures that the group satisfies the strong Tits alternative, provided that each vertex stabiliser satisfies the strong Tits alternative. We use it to prove that all Artin groups of type FC satisfy the strong Tits alternative.

中文翻译：

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FC 类型的 Artin 组的山雀替代品

摘要 给定对有限维 CAT ⁢ ( 0 ) {\mathrm{CAT}(0)} 立方体复形的群作用，我们给出了一个简单的标准，纯粹用立方体稳定器来表达，以确保该群满足强 Tits 选择，前提是每个顶点稳定器都满足强 Tits 替代方案。我们用它来证明所有 FC 类型的 Artin 群都满足强 Tits 选择。