群与设计研究综述  

A Survey of Groups and Designs

作　　者：田德路 黄铮 刘伟俊[3,4] 周胜林 TIAN Delu;HUANG Zheng;LIU Weijun;ZHOU Shenglin(School of Mathematics,Guangdong University of Education Guangzhou,Guangdong,510303,P.R.China;School of Mathematics and Statistics,Hunan University of Science and Technology,Xiangtan,Hunan,411201,P.R.China;School of Mathematics and Statistics,Central South University,Changsha,Hunan,410083,P.R.China;School of Basic Education,Guangdong University of Science and Technology,Dongguan,Guangdong,523083,P.R.China;School of Mathematics,South China University of Technology,Guangzhou,Guangdong,510641,P.R.China)

机构地区：[1]广东第二师范学院数学学院,广东广州510303 [2]湖南科技大学数学与统计学院,湖南湘潭411201 [3]中南大学数学与统计学院,湖南长沙410083 [4]广东科技学院通识教育学院,广东东莞523083 [5]华南理工大学数学学院,广东广州510641

出　　处：《数学进展》2025年第2期265-291,共27页Advances in Mathematics(China)

基　　金：国家自然科学基金(Nos.12271173,12471022,12401020,12071092)。

摘　　要：群论与设计理论联系紧密.自有限单群分类问题解决以来,抽象群和置换群的一些重大公开问题先后获得了解决,使得群与设计的联系的研究更为活跃.本文对近三十年来具有区传递和旗传递自同构群的设计的研究进展进行综述,并提出了若干值得研究的问题.Group theory and design theory have very fruitful connections.Many important open questions of finite groups and permutation groups have been solved post-CFSG,which make the research of groups and designs more active.This paper gives a summary of the research and advancement on block transitive and flag transitive designs in recent 30 years and propose some questions for further study.

关 键 词：设计 自同构 本原群 区传递 旗传递 

分 类 号：O152.1[理学—数学] O157.2[理学—基础数学]