Let G be a random torsion-free nilpotent group generated by two random words of length l in Un(Z). Letting l grow as a function of n, we analyze the step of G, which is bounded by the step of Un(Z). We prove a conjecture of Delp, Dymarz, and Schafer-Cohen, that the threshold function for full step is l = n. A group G is nilpotent if its lower central series G = G0 ≥ G1 ≥ · · · ≥ Gr = {0} defined byGi+1 = [G,Gi], eventually terminates. The first index r for whichGr = 0 is called the step of G… Expand

We study random torsion-free nilpotent groups generated by a pair of random words of length $\ell$ in the standard generating set of $U_n(\mathbb{Z})$. Specifically, we give asymptotic results about… Expand

We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the length tend to… Expand