On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups

Zhang, Zhilin1; Chen, Jianfu2; Zhou, Shenglin3

2023-11-01

10.1002/jcd.21924

JOURNAL OF COMBINATORIAL DESIGNS   影响因子和分区

1063-8539

1520-6610

Let D = (P, B) be a nontrivial symmetric (v, k, lambda)design with lambda <= 100, and let G be a flag-transitive automorphism group of D. In this paper, we show that if G is quasiprimitive on P, then G is of holomorph affine or almost simple type. Moreover, if G is imprimitive on P, then G is of almost simple type. According to this observation and to the classification of the finite simple groups we determine all such symmetric designs and the corresponding automorphism groups. We conclude with two open problems and a conjecture.

flag-transitive imprimitive groups O'Nan-Scott theorem quasiprimitive permutation groups symmetric designs

SCI ; EI

英语

通讯

The authors would like to thank Professor P.-H. Zieschang at University of Texas Rio Grande and the anonymous referees for corrections and valuable comments that led to the improvement of the paper. This work was supported by the National Natural Science F["12001204","12271173"] ; National Natural Science Foundation of China[2023A04J0009]

Mathematics

Mathematics

WOS:001098759000001

WILEY

MATHEMATICS

2-s2.0-85176130813

Web of Science

1.South China Normal Univ, Sch Math Sci, Guangzhou 510640, Guangdong, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
3.South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China

Zhang, Zhilin,Chen, Jianfu,Zhou, Shenglin. On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups[J]. JOURNAL OF COMBINATORIAL DESIGNS,2023,32(3):107-126.

Zhang, Zhilin,Chen, Jianfu,&Zhou, Shenglin.(2023).On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups.JOURNAL OF COMBINATORIAL DESIGNS,32(3),107-126.

Zhang, Zhilin,et al."On symmetric designs with flag-transitive and point-quasiprimitive automorphism groups".JOURNAL OF COMBINATORIAL DESIGNS 32.3(2023):107-126.