Block‐Transitive and Point‐Primitive 2‐   (  v  ,  k  ,  2  )    Designs with Sporadic Socle | Zendy

Zhang Xiaohong | Zendy; Zhou Shenglin | Zendy

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Block‐Transitive and Point‐Primitive 2‐ ( v , k , 2 ) Designs with Sporadic Socle

Author(s) -

Zhang Xiaohong,

Zhou Shenglin

Publication year - 2017

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.21528

Subject(s) - socle , mathematics , transitive relation , block (permutation group theory) , combinatorics , point (geometry) , paleontology , geometry , geology , inversion (geology) , structural basin

The purpose of this paper is to classify all pairs ( D , G ) , where D is a nontrivial 2‐ ( v , k , 2 ) design, and G ≤ A u t ( D ) acts transitively on the set of blocks of D and primitively on the set of points of D with sporadic socle. We prove that there exists only one such pair ( D , G ) : D is the unique 2‐(176,8,2) design and G = H S , the Higman–Sims simple group.

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