Subgroup growth in free class-2-nilpotent groups

We describe an effective procedure to compute the local subgroup zeta functions of the free class-2-nilpotent groups on d generators, for all d≥2. For d=4, this yields a new, explicit formula. For d∈{4,5}, we compute the topological subgroup zeta functions. We also obtain general results about the reduced and topological subalgebra zeta functions. For the former, we determine the behaviour at one; for the latter, the degree and behaviours at zero and infinity. Some of these results confirm, in the relevant special cases, general conjectures by Rossmann.