Random Nilpotent Groups of Maximal Step

Publication date: 16 January 2022

Abstract: Let

G

be a random torsion-free nilpotent group generated by two random words of length

e l l

in

U_{n} (m a t h b b Z)

. Letting

e l l

grow as a function of

n

, we analyze the step of

G

, which is bounded by the step of

U_{n} (m a t h b b Z)

. We prove a conjecture of Delp, Dymarz, and Schafer-Cohen, that the threshold function for full step is

e l l = n^{2}

.

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