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arXiv · 2201.06033

Random Nilpotent Groups of Maximal Step

Phillip Harris
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Abstract

Let $G$ be a random torsion-free nilpotent group generated by two random words of length $\ell$ in $U_n(\mathbb{Z})$. Letting $\ell$ grow as a function of $n$, we analyze the step of $G$, which is bounded by the step of $U_n(\mathbb{Z})$. We prove a conjecture of Delp, Dymarz, and Schafer-Cohen, that the threshold function for full step is $\ell = n^2$.

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Phillip Harris. 2022-01-16. Random Nilpotent Groups of Maximal Step. https://arxiv.org/abs/2201.06033

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