The most symmetric smooth cubic surface over a finite field of characteristic 2

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-07-13 DOI:10.1016/j.ffa.2024.102470

Anastasia V. Vikulova

引用次数: 0

Abstract

In this paper we find the largest automorphism group of a smooth cubic surface over any finite field of characteristic 2. We prove that if the order of the field is a power of 4, then the automorphism group of maximal order of a smooth cubic surface over this field is ${PSU}_{4} (F_{2})$ . If the order of the field of characteristic 2 is not a power of 4, then we prove that the automorphism group of maximal order of a smooth cubic surface over this field is the symmetric group of degree 6. Moreover, we prove that smooth cubic surfaces with such properties are unique up to isomorphism.

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特征为 2 的有限域上最对称的光滑立方曲面

在本文中，我们找到了任意有限特征域 2 上光滑立方曲面的最大自变群。我们证明，如果域的阶是 4 的幂次，那么该域上光滑立方曲面的最大阶自形群是 PSU4(F2)。如果特征 2 场的阶不是 4 的幂次，那么我们证明该场上光滑立方体曲面的最大阶自形群是 6 度对称群。此外，我们还证明了具有这种性质的光滑立方体曲面在同构时是唯一的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.