Around subgroups of Artin groups: derived subgroups and acylindrical hyperbolicity in the even FC-case

This is the authors' abstract. We don't add key points for this paper.

We generalize to (certain) Artin groups some results previously known for right-angled Artin groups (RAAGs).First, we generalize a result by Droms, B. Servatius, and H. Servatius, and prove that the derived subgroup of an Artin group is free if and only if the group is coherent.Second, coherent Artin groups over noncomplete graphs split as free amalgamated products along free abelian subgroups, and we extend to arbitrary Artin groups admitting such a splitting a recent result by Casals-Ruiz and Lopez de Gamiz Zearra on finitely generated normal subgroups of RAAGs.Finally, we use splittings of even Artin groups of FC-type to generalize results of Minasyan and Osin on acylindrical hyperbolicity of their subgroups.