We prove 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.
Cite this article
Constantin Gonciulea, Infinite Coxeter groups virtually surject onto ℤ. Comment. Math. Helv. 72 (1997), no. 2, pp. 257–265DOI 10.1007/S000140050015