Enumerating finite class-2-nilpotent groups on 2 generators

2009/08/10 by Christopher Voll, Voll, Christopher
Mathematics · #05A15 #20E34 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.GR #msc:05A15 #msc:20E34

paper · pdf · doi:10.48550/arxiv.0908.1355

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

openalex publication_date 2009/08/10 · arxiv created 2009/11/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ∑_n=1^∞ g(n,2,2)n^-s.

Citations

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

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