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In this paper we prove that there is no biplane admitting a flag-transitive automorphism group of almost simple type, with exceptional socle of Lie type. A biplane is a (v,k,2)-symmetric design, and a flag is an incident point-block pair. A group G is almost simple with socle X if X is the product of all the minimal normal subgroups of G, and X⊴G≤Aut (G).    Throughout this work we use the classification of finite simple groups, as well as results from P.B. Kleidman’s Ph.D. thesis which have not been published elsewhere.

Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type