Power series coefficients for probabilities in finite classical groups

John R. Britnell, Jason Fulman

Published 2005-11-15Version 1

It is shown that a wide range of probabilities and limiting probabilities in finite classical groups have integral coefficients when expanded as a power series in 1/q. Moreover it is proved that the coefficients of the limiting probabilities in the general linear and unitary cases are equal modulo 2. The rate of stabilization of the finite dimensional coefficients as the dimension increases is discussed.