论文标题
最大步骤的随机nilpotent组
Random Nilpotent Groups of Maximal Step
论文作者
论文摘要
令$ g $为一个随机的无扭转的nilpotent组，由两个随机单词$ \ ell $ in $ u_n（\ mathbb {z}）$生成。让$ \ ell $随着$ n $的函数而生长，我们分析了$ g $的步骤，该步骤受$ u_n（\ Mathbb {z}）$的步骤。我们证明了Delp，Dymarz和Schafer-Cohen的猜想，完整步骤的阈值函数为$ \ ell = n^2 $。
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 $\ell = n^2$.
