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Alternating groups and flag-transitive 2-(v, k, 4) symmetric designs

✍ Scribed by Huili Dong; Shenglin Zhou

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 129 KB
Volume: 19
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20294

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✦ Synopsis

In this article, we study the classification of flag-transitive, point-primitive 2-(v, k, 4) symmetric designs. We prove that if the socle of the automorphism group G of a flag-transitive, point-primitive nontrivial 2-(v, k, 4) symmetric design D is an alternating group A n for n ≥ 5, then (v, k) = (15, 8) and D is one of the following: (i) The points of D are those of the projective space PG(3, 2) and the blocks are the complements of the planes of PG(3, 2), G = A 7 or A 8 , and the stabilizer G x of a point x of D is L 3 (2) or AGL 3 (2), respectively. (ii) The points of D are the edges of the complete graph K 6 and the blocks are the complete bipartite subgraphs K 2,4 of K 6 ,

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