The boundary and the virtual cohomological dimension of Coxeter groups (Q2725461)

The purpose of this paper is to study Coxeter groups and their boundaries.NEWLINENEWLINENEWLINEIn the first part, the authors give some properties of the virtual cohomological dimension of Coxeter groups over principal ideal domains. The second part concerns the construction of a sequence of parabolic subgroups \(\Gamma_{W_0}\subset\cdots\subset\Gamma_{W_{n-1}}\) of a right-angled Coxeter group \(\Gamma\) with \(\text{vcd}_R\Gamma=n\); this sequence is such that \(\text{vcd}_R\Gamma_{W_i}=i\). In the third part, the authors show that a parabolic subgroup of a right-angled Coxeter group is of finite index if and only if their boundaries coincide.