Equalities on the number of conjugacy classes of the Sylow p-subgroups of GL(n, q)

摘要

We denote by Gn the group of the upper unitriangular matrices over F-q, the finite field with q = p (t) elements, and r(G (n)) the number of conjugacy classes of G (n). In this paper, we obtain the value of r(G (n)) modulo (q (2) -1)(q -1). We prove the following equalities