Given an odd prime number p and a Coxeter group W such that the order of the product st is prime to p for all Coxeter generators s, t of W, we prove that the p-local homology groups H-k(W, Z((p))) vanish for 1 <= k <= 2(p - 2). This generalizes a known vanishing result for symmetric groups due to Minoru Nakaoka.
This is the peer reviewed version of the following article: Akita, T. (2016), A vanishing theorem for the p-local homology of Coxeter groups. Bulletin of the London Mathematical Society, 48: 945–956, which has been published in final form at doi:10.1112/blms/bdw063. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.