Subgroup growth in free class-2-nilpotent groups

2023/05/31 by Viola Siconolfi, Siconolfi, Viola, Marlies Vantomme +3
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2305.19665

openalex publication_date 2023/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. For d=4, this yields a new, explicit formula. For d∈\4,5\, we compute the topological subgroup zeta function. We also obtain general results about the reduced and topological subalgebra zeta functions. For the former, we determine the behaviour at one and for the latter, the degree and behaviours at zero and infinity. Some of these results confirm, in the relevant special cases, general conjectures by T. Rossmann.

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