Even Artin Groups

Abstract

Right-angled Artin groups form an interesting family of groups both from analgebraic and a topological point of view. There are a lot of well-known propertiesof right-angled Artin groups: for example they are poly-free, locallyindicable, right orderable and residually finite. Besides, also many importantproblems are well understood for these groups such as the word problem, therigidity problem, Serre's question or the K(pi, 1) conjecture.In this thesis, we will study some of these properties for a bigger andinteresting subfamily of Artin groups: even Artin groups. We generalizemany of these properties either for even Artin groups in full genarility or forsome big and interesting subfamilies.In particular, we prove that even Artin groups of FC type and large evenArtin groups are poly-free (which, as we will see, implies that they are alsolocally indicable and right orderable) and that even Artin groups of FC typeand general Artin groups based on trees are residually finite. Finally, weanswer Serre's question for the whole family of even Artin groups.<br /