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.

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Probability theory on algebraic and topological structures (60B99)

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