A class of rigid Coxeter groups

الأصل · EN

In this paper, we give a new class of rigid Coxeter groups. Let (W,S) be a Coxeter system. Suppose that (0) for each s,t∈ S such that m(s,t) is even, m(s,t)=2, (1) for each s≠ t∈ S such that m(s,t) is odd, {s,t} is a maximal spherical subset of S, (2) there does not exist a three-points subset {s,t,u}⊂ S such that m(s,t) and m(t,u) are odd, and (3) for each s≠ t∈ S such that m(s,t) is odd, the number of maximal spherical subsets of S intersecting with {s,t} is at most two, where m(s,t) is the order of st in the Coxeter group W. Then we show that the Coxeter group W is rigid. This is an extension of a result of D.Radcliffe.