Infinite Coxeter groups virtually surject onto \(\mathbb{Z}\)
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)].
scientific article; zbMATH DE number 1121230