"Subgroups of right-angled Artin groups"
Lopez de Gamiz Zearra, JoneIn general, subgroups of right-angled Artin groups (RAAGs for short) are known to have a wild structure and bad algorithmic behaviour. In this talk we will see that restricting to important families of RAAGs, however, assures a tame subgroup structure that leads to good algorithmic behaviour. First of all, we will discuss finitely generated normal subgroups of RAAGs. A classical result of Greenberg states that non-trivial finitely generated normal subgroups of free groups are of finite index. We will generalise this result to the class of RAAGs and show that finitely generated normal subgroups of RAAGs are virtually co-abelian. We will then discuss some algorithmic consequences such as the decidability of the conjugacy and the membership problems for these subgroups. Secondly, we will recall some results on subgroups of direct products of free groups developed by Baumslag-Roseblade and Bridson-Howie-Miller-Short and we will explain how they generalise to other classes of RAAGs such as coherent RAAGs. This is joint work with Montserrat Casals-Ruiz (University of the Basque Country UPV/EHU).