Normal subgroup growth in free class-2-nilpotent groups

Abstract

Let $F_{2,d}$ denote the free class-2-nilpotent group on $d$ generators. We compute the normal zeta functions ${\zeta }_{F_{2,d}}^{◃}(s)$, prove that they satisfy local functional equations and determine their abscissae of convergence and pole orders.

14 pages