Torsion elements of the Nottingham group of order p^2

Abstract

We establish an explicit upper bound B(p,l,m), depending on p,l,m, on the number of conjugacy classes of order p^2 torsion elements u of type <l,m> of the Nottingham group defined over the prime field of characteristic p >0. In the cases where l < p, the number of conjugacy classes of type <l,m> coincides with B(p,l,m). Moreover, we give a criterion on when u and u^n are conjugate.