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Infinite Coxeter groups virtually surject onto $ \Bbb {Z} $

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Commentarii Mathematici Helvetici

Abstract.

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.

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Received: July 1, 1996

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Gonciulea, C. Infinite Coxeter groups virtually surject onto $ \Bbb {Z} $. Comment. Math. Helv. 72, 257–265 (1997). https://doi.org/10.1007/s000140050015

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  • DOI: https://doi.org/10.1007/s000140050015

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