Flag-transitive, point-imprimitive 2-designs and direct products of symmetric groups

Chen, Jianfu1; Zhou, Shenglin2; Shen, Jiaxin3

2024-04-05

10.37236/11002

ELECTRONIC JOURNAL OF COMBINATORICS   影响因子和分区

1077-8926

Consider the direct product of symmetric groups S(c)x S-n and its natural action on P = C x N, where |C| = c and |N| = n. We characterize the structure of 2 -designs with point set P admitting flag -transitive, point-imprimitive automorphism groups H <= S(c)x S-n. As an example of its applications, we show that H cannot be any subgroup of D(2c )x S-n or S-c x D-2n. Besides, some families of 2 -designs admitting flag-transitive automorphism groups S(c)x S-n are constructed by using complete bipartite graphs and cycles. Two families of these also admit flag -transitive, point -primitive automorphism groups S-c(sic) S-2, a family of which attain the Cameron -Praeger upper bound v = (k - 2)(2).

SCI

英语

第一

National Natural Science Foundation of China["12201469","12271173"]

Mathematics

Mathematics, Applied ; Mathematics

WOS:001201728600001

ELECTRONIC JOURNAL OF COMBINATORICS

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
2.South China Univ Technol, Sch Math, Guangzhou, Guangdong, Peoples R China
3.Wuyi Univ, Sch Math & Comp Sci, Jiangmen, Guangdong, Peoples R China

Chen, Jianfu,Zhou, Shenglin,Shen, Jiaxin. Flag-transitive, point-imprimitive 2-designs and direct products of symmetric groups[J]. ELECTRONIC JOURNAL OF COMBINATORICS,2024,31(2).

Chen, Jianfu,Zhou, Shenglin,&Shen, Jiaxin.(2024).Flag-transitive, point-imprimitive 2-designs and direct products of symmetric groups.ELECTRONIC JOURNAL OF COMBINATORICS,31(2).

Chen, Jianfu,et al."Flag-transitive, point-imprimitive 2-designs and direct products of symmetric groups".ELECTRONIC JOURNAL OF COMBINATORICS 31.2(2024).