Parabolic subgroups of Artin groups of type FC. (Q1880017)
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scientific article; zbMATH DE number 2101051
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Parabolic subgroups of Artin groups of type FC. |
scientific article; zbMATH DE number 2101051 |
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Parabolic subgroups of Artin groups of type FC. (English)
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16 September 2004
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Let \((A,S)\) be an Artin group of type FC and \(A_T\) a standard parabolic subgroup of \(A\). The author uses combinatorial tools to show that the normalizer of \(A_T\), the commensurator of \(A_T\), and the product of the quasi-centralizer of \(A_T\) by \(A_T\) are equal. Furthermore, the author shows that the centralizer and the quasi-centralizer of \(A_T\) in \(A\) are generated by their intersections with the monoid \(A^+\).
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Artin groups
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parabolic subgroups
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commensurators
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subgroups of finite index
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normalizers
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quasi-centralizers
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