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Phillip Harris
Random nilpotent groups of maximal step
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| Published: |
October 9, 2022. |
| Keywords: |
random groups, nilpotent groups, lower central series. |
| Subject [2010]: |
20D15, 20P05, 60B15. |
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Abstract
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 Schaffer-Cohen, that the threshold function for full step is L = n2.
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| Acknowledgements
We thank Tullia Dymarz for suggesting this problem and for many helpful discussions. This research was supported by NSF grants DMS-2037851 and DMS-1902173.
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| Author information
Phillip Harris:
101-05 Van Vleck Hall
University of Wisconsin
Madison, WI 53706, USA
plharris@wisc.edu
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