A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ

Jordan S. Ellenberg, Julianna Tymoczko

Type: Article

Publication Date: 2010-01-01

Citations: 1

DOI: https://doi.org/10.1515/forum.2010.018

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).

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+	Random Walks on Finite Groups	2004	Laurent Saloff‐Coste
+	Introduction to Lie Algebras and Representation Theory	1972	James E. Humphreys
+	Linear Algebraic Groups	1975	James E. Humphreys
+	Linear Algebraic Groups	1998	T. A. Springer
+ PDF Chat	Growth and generation in SL<sub>2</sub>(ℤ∕pℤ)	2008	H. A. Helfgott
+ PDF Chat	Random Walks on the Groups of Upper Triangular Matrices	1995	Richard Stong
+	Moderate growth and random walk on finite groups	1994	Persi Diaconis L. Saloff‐Coste
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+ PDF Chat	Comparison Techniques for Random Walk on Finite Groups	1993	Persi Diaconis Laurent Saloff‐Coste
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