一般域上辛群的对合积（II）：有限域

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-05-08 DOI:10.1016/j.ffa.2025.102641

Clément de Seguins Pazzis

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引用次数: 0

摘要

设s是特征为非2的域F上的n维辛形式，特征为n>；2。在上一篇文章中，我们证明了如果F是无限的，那么辛群Sp(s)的每一个元素都是四个对合的乘积，如果n是4的倍数，否则是五个对合的乘积。在这里，我们将这个结果适用于所有特征为非2的有限域，除了n=4和|F|=3的特殊情况，这是我们广泛研究的特殊情况。

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Products of involutions in symplectic groups over general fields (II): Finite fields

Let s be an n-dimensional symplectic form over a field

F

of characteristic other than 2, with

n > 2

In a previous article, we have proved that if

F

is infinite then every element of the symplectic group

Sp (s)

is the product of four involutions if n is a multiple of 4 and of five involutions otherwise.

Here, we adapt this result to all finite fields with characteristic not 2, with the sole exception of the very special situation where

n = 4

and

| F | = 3

, a special case which we study extensively.

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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.