浙江大学学报（理学版）2024，Vol.51Issue(3)：265-272,8.DOI:10.3785/j.issn.1008-9497.2024.03.002
区传递Steiner t-设计与散在单群
Block-transitive Steiner t-designs and sporadic simple groups
摘要
Abstract
The study of t-designs with certain highly symmetric properties and the classification of their automorphism groups is one of the important topics of algebraic combinatorics.Hitherto the classification of flag-transitive Steiner t-designs has been completely settled by Huber.Nevertheless,it is interesting that the results of t-designs will get richer when G-flag-transitivity are weakened to G-block-transitivity and the research work becomes more challenging as well.Depending on the classification of finite simple groups and 2-transitive permutation groups,we show the classification of block-transitive Steiner t-designs admitting a block-transitive automorphism group with sporadic socle,and draw a conclusion as follows:Let D=(P,E)be a non-trivial Steiner t-design and G≤Aut(D)be point-primitive.If the socle of G is a sporadic simple group,then G acts block-transitively on D if and only if G acts flag-transitively on D,and D is one of the five known flag-transitive Steiner t-designs.关键词
Steiner t-设计/区传递/点本原/散在单群Key words
Steiner t-designs/block-transitive/point-primitive/sporadic simple group分类
数理科学引用本文复制引用
庞璇,詹小秦..区传递Steiner t-设计与散在单群[J].浙江大学学报（理学版）,2024,51(3):265-272,8.基金项目
国家自然科学基金资助项目(12361004) （12361004）
江西省自然科学基金资助项目(20224BAB211005). （20224BAB211005）
