2005/10/24 by Tetsuya Hosaka, Hosaka, Tetsuya
Mathematics · #20F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.math/0510510
openalex publication_date 2005/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we show that the center of every Coxeter group is finite and isomorphic to (\Z2)n for some n≥ 0. Moreover, for a Coxeter system (W,S), we prove that Z(W)=Z(W_S∖S) and Z(W_S)=1, where Z(W) is the center of the Coxeter group W and S is the subset of S such that the parabolic subgroup W_S is the \it essential parabolic subgroup of (W,S) (i.e. W_S is the minimum parabolic subgroup of finite index in (W,S)). The finiteness of the center of a Coxeter group implies that a splitting theorem holds for Coxeter groups.