For each d ∈ N we construct a 3-generated group Hd, which is a subdirect product of free groups, such that the cohomological dimension of Hd is d. Given a group F and a normal subgroup N C F we prove that any right angled Artin group containing the special HNN-extension of F with respect to N must also contain F/N . We apply this to construct, for every d ∈ N, a 4-generated group Gd, embeddable...
