Torsion elements of the Nottingham group of order $p^2$ and type $\langle 2, m \rangle$

TL;DR

This paper classifies specific torsion elements of order p^2 in the Nottingham group over a prime field, enhancing understanding of its algebraic structure.

Contribution

It provides a complete classification of torsion elements of order p^2 and type ⟨2, m⟩ in the Nottingham group, a previously unresolved problem.

Findings

Classification of torsion elements of order p^2

Explicit description of elements of type ⟨2, m⟩

Advancement in understanding Nottingham group's structure

Abstract

We classify torsion elements of order $p^2$ and type $\langle 2, m \rangle$ in the Nottingham group defined over a prime field of characteristic $p >0$.