Automorphisms of right-angled Artin groups

Nakajima, p-ranks and automorphism groups of algebraic curves, TransB. Raynaud, p-groupes et réduction semi-stable des courbes, The Grothendieck Festschrift, Vol.3,

Proof. — Use induction from, say, abelian subgroups. For the latter, since the exponent is either 4 or 6, the numbers of irreducible real and rational representations coincide. But

The group Aut( U ) may be huge ( U could be the affine space), but there are techniques to study groups of au- tomorphisms that are not available for birational transformations;

is finitely generated, abelian-by-finite and centralized by a finite index subgroup of Out (Γ). The case of a general polycyclic-by-finite group. — In this subsection, we ex- plain

1. Goxeter, Shephard and Artin groups. Local deformation theory of representations. The correspondence between projective reflections and their fixed points. Commuting and

By induction on the derived length of N, we deduce that N=L 0 is an extension of a group of fe; c; kg-bounded exponent by a nilpotent group of fe; c; kg-bounded class, say c 2.. We

Since the standard action of a right-angled Artin group on its associated CAT(0) cube complex is RAAG-like, with all non-trivial elements acting hyperbolically, the following

Using Theorem 25, we now identify these groups with those given in the classification of 4-dimensional almost-Bieberbach groups with 2-step nilpotent sub- group given in [De,