A Sharp Diameter Bound for Unipotent Groups of Classical Type Overℤ /pℤ

Authors

Jordan S. Ellenberg, University of Wisconsin
Julianna Tymoczko, University of IowaFollow

Document Type

Article

Publication Date

3-1-2010

Publication Title

Forum Mathematicum

Abstract

The unipotent subgroup of a finite group of Lie type over a prime field Fp comes equipped with a natural set of generators; the properties of the Cayley graph associated to this set of generators have been much studied. In the present paper, we show that the diameter of this Cayley graph is bounded above and below by constant multiples of np + n2 log p, where n is the rank of the associated Lie group. This generalizes the result of Ellenberg, A sharp diameter bound for an upper triangular matrix group, Harvard University, 1993, which treated the case of SLn(Fp).

Volume

22

Issue

2

First Page

327

Last Page

347

DOI

10.1515/FORUM.2010.018

ISSN

09337741

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Ellenberg, Jordan S. and Tymoczko, Julianna, "A Sharp Diameter Bound for Unipotent Groups of Classical Type Overℤ /pℤ" (2010). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/107