Intrinsic reflections in Coxeter systems

Let (W,S)(W,S) be a Coxeter system and let s∈Ss∈S. We call s   a right-angled generator of (W,S)(W,S) if st=tsst=ts or st   has infinite order for each t∈St∈S. We call s an intrinsic reflection of W   if s∈RWs∈RW for all Coxeter generating sets R of W  . We give necessary and sufficient conditions for a right-angled generator s∈Ss∈S of (W,S)(W,S) to be an intrinsic reflection of W.