On the Center of a Coxeter Group
نویسنده
چکیده
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\S̃) and Z(W S̃ ) = 1, where Z(W ) is the center of the Coxeter group W and S̃ is the subset of S such that the parabolic subgroup W S̃ is the essential parabolic subgroup of (W, S) (i.e. W S̃ 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.
منابع مشابه
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