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Flag‐Transitive 2‐ Symmetric Designs with Sporadic Socle
Authors:Delu Tian  Shenglin Zhou
Institution:1. Department of Mathematics, South China University of Technology, Guangdong, P. R. China;2. Department of Mathematics, Guangdong University of Education, Guangdong, P. R. China
Abstract:Let urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0003 be a nontrivial 2‐urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0004 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 urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0005 must be one of the following: a 2‐(144, 66, 30) design with urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0006 or urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0007, a 2‐(176, 50, 14) design with urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0008, a 2‐(176, 126, 90) design with urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0009 or urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0010, or a 2‐(14,080, 12,636, 11,340) design with urn:x-wiley:10638539:media:jcd21385:jcd21385-math-0011.
Keywords:symmetric design  flag‐transitive  point‐primitive  sporadic simple groupMR(2000) Subject Classification 05B05  05B25  20B25  20D08
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