On the Asymptotics of the Growth of 2-Step Nilpotent Groups
Michael Stoll · Journal of the London Mathematical Society · 1998
Pansu has shown that the growth function of every virtually nilpotent group Γ with respect to any finite generating set has asymptotics γ(n)∼αnd, where d is the degree of growth of Γ. The paper refines his result in the special case of 2-step nilpotent groups to obtain γ(n)=αnd+O(nd−1).