Torsion elements of the Nottingham group of order p²

2018/10/26 by Chun Yin Hui, Hui, Chun Yin, Krishna Kishore +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #Finite Group Theory Research #math.GR #math.NT

paper · pdf · doi:10.48550/arxiv.1810.11304

10 pages

arxiv created 2018/10/26 · arxiv updated 2018/10/29

Abstract

We establish an explicit upper bound B(p,l,m), depending on p,l,m, on the number of conjugacy classes of order p² 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 uⁿ are conjugate.

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