A probabilistic approach toward the finite general linear and unitary groups

Details A probabilistic approach toward the finite general linear and unitary groups A probabilistic approach toward the finite general linear and unitary groups

1997-12-09

arxiv.org/abs/math/9712238v1

Mathematics

Group Theory

14 pages

Scientific paper

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.

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