Texas A&M University, Department of
Mathematics, 216 Milner Hall, 10th of March 2004, 4:00-5:00
Groups and Dynamcs Seminar
Poly-free
constructions for right-angled Artin groups
Zoran Sunik of Texas A&M University
A group H is poly-free if it has a subnormal series in which all
factors are free. Equivalently, H is a finitely iterated semidirect
product of free groups. The shortest length of a subnormal series with
free factors is called the poly-free length of H.
We show that all right-angled Artin groups are poly-free. The poly-free
length of a right-angled Artin group AG is bounded between the clique
number and the chromatic number of the graph G that defines the group
AG. These bounds are sharp.
A complete characterization of graphs that define right-angled Artin
groups of poly-free length 2 is given. Such graphs must have an
independent set of vertices D such that every cycle in G contains at
least two vertices from D.
In case of poly-free right-angled Artin groups of poly-free length 2,
both free factors are finitely generated if and only if the defining
graph is a tree or a complete bipartite graph.
This joint work with Susan Hermiller is motivated by a question of
Bestvina asking if all Artin groups are virtually poly-free.