Automorphisms of Right-Angled Coxeter Groups

Abstract EN

If (W,S) is a right-angled Coxeter system, then Aut(W) is a semidirect product of the group Aut∘(W) of symmetric automorphisms by the automorphism group of a certain groupoid.

We show that, under mild conditions, Aut∘(W) is a semidirect product of Inn(W) by the quotient Out∘(W)=Aut∘(W)/Inn(W).

We also give sufficient conditions for the compatibility of the two semidirect products.

When this occurs there is an induced splitting of the sequence 1→Inn(W)→Aut(W)→Out(W)→1 and consequently, all group extensions 1→W→G→Q→1 are trivial.