有限域上特殊矩阵群性质  

On the Properties of Special Matrix Groups over Finite Fields

作　　者：何晴 赵正俊 HE Qing;ZHAO Zhengjun(School of Mathematics and Physics,Anqing Normal University,246133,Anqing,Anhui,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《淮北师范大学学报(自然科学版)》2025年第1期6-9,共4页Journal of Huaibei Normal University:Natural Sciences

基　　金：国家自然科学基金项目(11971382);安徽省高校学科(专业)拔尖人才项目。

摘　　要：为丰富有限域上矩阵群性质,通过有限域上射影一般线性群和射影特殊线性群关系,从群论角度明确给出这2类群阶数公式。同时,明确构造有限域上一般线性群Sylow p-子群,并证明有限域上二阶特殊线性群Sylow p-子群是循环群。To enrich the properties of matrix groups over finite fields,the order formulae of these two types of are given by means of projective general linear groups and projective special linear groups on finite fields.Some special subgroups,such as Sylow p-subgroups of general linear group over finite fields were also discussed.The Sylow p-subgroups of special linear group of a second-order over finite field is proved to be a cyclic group.

关 键 词：有限域 射影特殊线性群 射影一般线性群 SYLOW子群 

分 类 号：O151.21[理学—数学]