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

Authors:
Eugenia O'Reilly-Regueiro
Affiliations:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, México, Mexico 04510
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2008

Citing 5
Cited 1

On finite linear spaces with almost simple flag-transitive automorphism groups

Journal of Combinatorial Theory Series A
On primitivity and reduction for flag-transitive symmetric designs

Journal of Combinatorial Theory Series A
Biplanes with flag-transitive automorphism groups of almost simple type, with alternating or sporadic socle

European Journal of Combinatorics
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)

Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Biplanes with flag-transitive automorphism groups of almost simple type, with classical socle

Journal of Algebraic Combinatorics: An International Journal

Flag-transitive symmetric 2-(96,20,4)-designs

Journal of Combinatorial Theory Series A

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Abstract

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驴G驴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.