A probabilistic approach toward the finite general linear and unitary groups
Abstract
Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's count of unipotent elements, Rudvalis and Shindoda's work on the fixed space of a random matrix, and Lusztig's work on counting nilpotent matrices of a given rank.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.math/9712238
 arXiv:
 arXiv:math/9712238
 Bibcode:
 1997math.....12238F
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Probability;
 20G40;
 60B99
 EPrint:
 14 pages