Flag‐Transitive 2‐     (  v  ,  k  ,  λ  )    Symmetric Designs with Sporadic Socle | Zendy

Tian Delu | Zendy; Zhou Shenglin | Zendy

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Flag‐Transitive 2‐ ( v , k , λ ) Symmetric Designs with Sporadic Socle

Author(s) -

Tian Delu,

Zhou Shenglin

Publication year - 2015

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.21385

Subject(s) - socle , mathematics , flag (linear algebra) , combinatorics , isomorphism (crystallography) , transitive relation , automorphism , automorphism group , symmetric group , pure mathematics , algebra over a field , inversion (geology) , paleontology , crystal structure , chemistry , structural basin , crystallography , biology

Let D be a nontrivial 2‐ ( v , k , λ ) symmetric design admitting a flag‐transitive, point‐primitive automorphism group G of almost simple type with sporadic socle. We prove that there are up to isomorphism six designs, and D must be one of the following: a 2‐(144, 66, 30) design with G = M 12orM 12 : 2 , a 2‐(176, 50, 14) design with G = H S , a 2‐(176, 126, 90) design with G = M 22or H S , or a 2‐(14,080, 12,636, 11,340) design with G = F i 22 .

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