Random Nilpotent Groups of Maximal Step

2022/01/16 by Phillip Harris, Harris, Phillip
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2201.06033

openalex publication_date 2022/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a random torsion-free nilpotent group generated by two random words of length ℓ in U_n(ℤ). Letting ℓ grow as a function of n, we analyze the step of G, which is bounded by the step of U_n(ℤ). We prove a conjecture of Delp, Dymarz, and Schafer-Cohen, that the threshold function for full step is ℓ = n².

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