Torsion elements of order p² in the Nottingham group

Abstract

© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020 C. Y. Hui is supported by China's Thousand Talents Plan: The Recruitment Program for Young Professionals. Let κ be a characteristic p finite field of q elements and q κ the Nottingham group over κ. Lubin associated to every conjugacy class of torsion element of κ a type. We establish an upper bound B (q; l, m) {B(q;l,m)} on the number of conjugacy classes of order p2 p2 torsion elements u of κ Nκl, m . In the case where l < p {l<p}, the bound B(q; l, m) {B(q;l,m)} is the exact number of conjugacy classes. Moreover, we give a criterion on when u and u n are conjugate.