Poly-free constructions for right-angled Artin groups

Details Poly-free constructions for right-angled Artin groups Poly-free constructions for right-angled Artin groups

2005-05-31

arxiv.org/abs/math/0505666v1

Mathematics

Group Theory

21 pages, 3 figures

Scientific paper

We show that every right-angled Artin group AG defined by a graph G of finite chromatic number is poly-free with poly-free length bounded between the clique number and the chromatic number of G. Further, a characterization of all right-angled Artin groups of poly-free length 2 is given, namely the group AG has poly-free length 2 if and only if there exists an independent set of vertices D in G such that every cycle in G meets D at least twice. Finally, it is shown that AG is a semidirect product of 2 free groups of finite rank if and only if G is a finite tree or a finite complete bipartite graph. All of the proofs of the existence of poly-free structures are constructive.

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