• Corpus ID: 246015916

# Random Nilpotent Groups of Maximal Step

@inproceedings{Harris2022RandomNG,
title={Random Nilpotent Groups of Maximal Step},
author={Phillip Harris},
year={2022}
}
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…

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