区传递Steiner t-设计与散在单群OA北大核心CSTPCD

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.