A vanishing theorem for the $p$-local homology of Coxeter groups

Abstract

Given an odd prime number $p$ and a Coxeter group $W$ such that the order of the product $st$ is prime to $p$ for every Coxeter generators $s,t$ of $W$, we prove that the $p$-local homology groups $H_k(W,{\mathbb{Z}}_{(p)})$ vanish for $1\le k\le 2(p-2)$. This generalize a known vanishing result for symmetric groups due to Minoru Nakaoka.

arXiv commentv2: minor changes (including the title). To appear in Bulletin of the London Mathematical Society

Cited by in corpus (1)

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