一类极大曲线族的自同构群
The Automorphism Groups of a Family of Maximal Curves
摘要：
Hasse Weil界限制了定义在有限域上的曲线的点的数量;如果点的数量满足这个界，则该曲线被称为极大曲线。Giulietti和Kommaros引入了一条在F_{q^6}上极大的曲线C_3，并确定了它的自同构群. Garcia，Guneri和Stichtenoth将这种构造推广到一族曲线C_n，其指数为大于或等于3的奇数n，使得C_n在F_{q^{2n}}上极大。本文确定了n > 3时的自同构群Aut（C_n），与n=3时的情形不同，它将C_n上的无穷远点固定在无穷远处.证明需要一个关于特征p中曲线的自同构群的新的结构性结果，使得每个Sylow p-子群恰好有一个不动点。MSC：11 G20，14 H37。
英文摘要：
The Hasse Weil bound restricts the number of points of a curve which are defined over a finite field; if the number of points meets this bound, the curve is called maximal. Giulietti and Korchmaros introduced a curve C_3 which is maximal over F_{q^6} and determined its automorphism group. Garcia, Guneri, and Stichtenoth generalized this construction to a family of curves C_n, indexed by an odd integer n greater than or equal to 3, such that C_n is maximal over F_{q^{2n}}. In this paper, we determine the automorphism group Aut(C_n) when n > 3; in contrast with the case n=3, it fixes the point at infinity on C_n. The proof requires a new structural result about automorphism groups of curves in characteristic p such that each Sylow p-subgroup has exactly one fixed point. MSC:11G20, 14H37.
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