Infinite Coxeter groups virtually surject onto \(\mathbb{Z}\) (Q1379580)
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scientific article; zbMATH DE number 1121230
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Infinite Coxeter groups virtually surject onto \(\mathbb{Z}\) |
scientific article; zbMATH DE number 1121230 |
Statements
Infinite Coxeter groups virtually surject onto \(\mathbb{Z}\) (English)
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6 January 1999
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It is proved that any infinite Coxeter group has a subgroup of finite index which homomorphically surjects onto the integers. This implies the known result that infinite Coxeter groups do not have property \((T)\) of Kazhdan [\textit{M. Bożejko}, \textit{T. Januszkiewicz} and \textit{R. J. Spatzier}, J. Oper. Theory 19, No. 1, 63-68 (1988; Zbl 0662.20040)].
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subgroups of finite index
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infinite Coxeter groups
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