Enumerating finite class-2-nilpotent groups on 2 generators

Abstract

We compute the numbers g(n,2,2) of nilpotent groups of order n, of class at most 2 generated by at most 2 generators, by giving an explicit formula for the Dirichlet generating function \sum_{n=1}^\infty g(n,2,2)n^{-s}.

5 pages. Minor revisions. To appear in C. R. Math. Acad. Sci. Paris

References in corpus (1)

• Zeta functions of groups and enumeration in Bruhat-Tits buildings