摘要
通过研究与群有关的齐次多项式,定义了有限群的复指标。复指标及其复表示的理论很快得到发展和完善起来。于是人们开始考虑有限域上的表示问题,即模表示论。对于有限群模表示论的基本问题是决定给定有限群的P-块代数的Morita等价类。当前国际上模表示论的研究主要围绕以下两个问题进行:一是刻画已知群,特别是有限单群的P-块代数的结构,二是对一般有限群的P-块代数进行定性的研究。而亏群在有限群模表示论的块理论中起到关键作用,它是联系群论性质和表示论性质最重要的对象,因此本文研究了一类有限群亏零块的存在性。利用子群的性质,给出了有限群存在亏零块的充要条件。
By studying homogeneous polynomials related to groups,the complex index of finite groups is defined.The theory of complex index and its complex representation has been developed and perfected quickly.So people began to consider the representation of finite fields,that is,modular representation theory.The basic problem of modular representation theory for finite groups is to determine the Morita equivalence class of p-block algebras of a given finite group.At present,the international research on model representation mainly focuses on the following two issues:One is to characterize the structure of p-block algebras of known groups,especially finite simple groups.The other is the qualitative study of p-block algebras of general finite groups.The deficient group plays a key role in the block theory of modular representation theory of finite groups.It is the most important object connecting the properties of group theory and representation theory.In this paper,we study the existence of zero deficient blocks of finite groups.By using the properties of subgroups,the necessary and sufficient conditions for the existence of null deficient blocks in finite groups are given.
作者
王宏
钱方生
WANG Hong;QIAN Fang-sheng(School of Mathematics, Heihe University, HeiHe 164300, China;School of Mathematics Science, Harbin Normal University, Harbin 150025, China)
出处
《哈尔滨理工大学学报》
CAS
北大核心
2020年第4期167-170,共4页
Journal of Harbin University of Science and Technology
基金
国家自然科学基金(11971134).
关键词
幂零群
亏零块
亏群
半正规子群
nilpotent group
p-block of defect 0
defect group
semi-normal subgroups
