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Flag‐transitive 2‐ ( v , 4 , λ ) designs of product type
Author(s) -
Zhan Xiaoqin,
Zhou Shenglin,
Chen Guangzu
Publication year - 2018
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21605
Subject(s) - mathematics , flag (linear algebra) , combinatorics , transitive relation , affine transformation , type (biology) , product (mathematics) , automorphism group , automorphism , simple (philosophy) , discrete mathematics , algebra over a field , pure mathematics , geometry , ecology , biology , philosophy , epistemology
In this paper, we prove that if a 2‐ ( v , 4 , λ ) design D admits a flag‐transitive automorphism group G , then G is of affine, almost simple type, or product type. Furthermore, we prove that if G is product type then D is either a 2‐(25, 4, 12) design or a 2‐(25, 4, 18) design withSoc ( G ) = A 5 × A 5 .