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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W. / Wilson, John S.

Managing Editor: Khukhro, Evgenii I. / Kramer, Linus

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Volume 18, Issue 4 (Jul 2015)


Longer nilpotent series for classical unipotent subgroups

Joshua Maglione
  • Department Of Mathematics, Colorado State University, Fort Collins, CO 80523, USA
  • Email:
Published Online: 2015-03-10 | DOI: https://doi.org/10.1515/jgth-2015-0008


In studying nilpotent groups, the lower central series and other variations can be used to construct an associated ℤ+-graded Lie ring, which is a powerful method to inspect a group. Indeed, the process can be generalized substantially by introducing ℕd-graded Lie rings. We compute the adjoint refinements of the lower central series of the unipotent subgroups of the classical Chevalley groups over the field ℤ/pℤ of rank d. We prove that, for all the classical types, this characteristic filter is a series of length Θ(d2) with nearly all factors having p-bounded order.

About the article

Received: 2014-04-04

Revised: 2014-07-02

Published Online: 2015-03-10

Published in Print: 2015-07-01

Citation Information: Journal of Group Theory, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgth-2015-0008. Export Citation

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