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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 , combinatorics , block (permutation group theory) , set (abstract data type) , point (geometry) , simple (philosophy) , block design , simple group , discrete mathematics , computer science , biology , geometry , paleontology , philosophy , inversion (geology) , epistemology , structural basin , programming language
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.