Counting formulas for certain p-subgroups of GL_n(F_p)

Abstract

Let p be a prime number and F_p a finite field of order p. Let GL_n(F_p) denote the general linear group and let U_n denote the unitriangular group of n x n upper triangular matrices with ones on the diagonal, over the finite field F_p. This is a finite group of order and a Sylow p-subgroup of GL_n(F_p}. In this work, we characterize some p-subgroups of GL_n(F_p) with respect to a given property.