Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type.
This paper completes the classification of symmetric \(2\)-\((v,k,2)\) designs, these are sometimes called biplanes, which have flag-transitive almost simple automorphism groups. The author, in a sequence of papers based on her Ph.D thesis [J. Comb. Theory, Ser. A 109, No. 1, 135-148 (2005; Zbl 1055.05014); Eur. J. Comb. 26, No. 5, 577-584 (2005; Zbl 1113.20003); J. Algebr. Comb. 26, No. 4, 529-552 (2007; Zbl 1126.05023)], has considered the other cases. The paper depends on some very detailed and specific information about the structure of maximal subgroups of the exceptional groups of Lie type. The combination of all these papers is that if \(D\) is a biplane with a primitive, flag-transitive automorphism group of almost simple type then \(D\) has parameters either \((7,4,2)\) or \((11,5,2)\) and is unique up to isomorphism.
scientific article; zbMATH DE number 5294576
scientific article