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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
Abstract 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 .