论允许向抛物面子群缩回的阿丁群

arXiv - MATH - Group Theory Pub Date : 2024-08-22 DOI:arxiv-2408.12291

Bruno Aaron Cisneros de la Cruz, María Cumplido, Islam Foniqi

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引用次数: 0

摘要

我们将偶数阿尔丁群的标准抛物面子群的回缩推广到 FC 型阿尔丁群和其他更一般的群族。我们证明这些回缩唯一地扩展到任何抛物线子群。我们利用溯源推广了 Antol\'in 和 Foniqi 的结果，这些结果将抛物线子群的交集问题简化为较弱的条件。作为推论，我们描述了 FC 情况下的一致性。

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On Artin groups admitting retractions to parabolic subgroups

We generalize the retractions to standard parabolic subgroups for even Artin groups to FC-type Artin groups and other more general families. We prove that these retractions uniquely extend to any parabolic subgroup. We use retractions to generalize the results of Antol\'in and Foniqi that reduce the problem of intersection of parabolic subgroups to weaker conditions. As a corollary, we characterize coherence for the FC case.

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arXiv - MATH - Group Theory

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