Torsion elements of order 𝑝2 in the Nottingham group
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AbstractLet κ be a characteristic p finite field of q elements and {\mathfrak{N}_{\kappa}} the Nottingham group over κ. Lubin associated to every conjugacy class of torsion element of {\mathfrak{N}_{\kappa}} a type. We establish an upper bound {B(q;l,m)} on the number of conjugacy classes of order {p^{2}} torsion elements u of {\mathfrak{N}_{\kappa}} of type {\langle l,m\rangle}. In the case where {l<p}, the bound {B(q;l,m)} is the exact number of conjugacy classes. Moreover, we give a criterion on when u and {u^{n}} are conjugate.
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1975 ◽
Vol 27
(4)
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pp. 837-851
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1996 ◽
Vol 39
(3)
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pp. 346-351
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1995 ◽
Vol 52
(3)
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pp. 431-439
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2004 ◽
Vol 69
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pp. 317-325
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2007 ◽
Vol 06
(03)
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pp. 469-475
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