On primitivity and reduction for flag-transitive symmetric designs

Authors:
Eugenia O'Reilly Regueiro
Affiliations:
Instituto de Matemáticas, Circuito Exterior, UNAM, México D.F. 04510, Mexico
Venue:
Journal of Combinatorial Theory Series A
Year:
2005

Citing 5
Cited 7

Design theory

Design theory
Flag-transitivity and primitivity

Discrete Mathematics
Finite linear spaces with flag-transitive groups

Journal of Combinatorial Theory Series A
Finite geometries

Finite geometries
Biplanes with flag-transitive automorphism groups of almost simple type, with alternating or sporadic socle

European Journal of Combinatorics

Biplanes with flag-transitive automorphism groups of almost simple type, with alternating or sporadic socle

European Journal of Combinatorics
Imprimitive flag-transitive symmetric designs

Journal of Combinatorial Theory Series A
The flag-transitive symmetric designs with 45 points, blocks of size 12, and 3 blocks on every point pair

Designs, Codes and Cryptography
Biplanes with flag-transitive automorphism groups of almost simple type, with classical socle

Journal of Algebraic Combinatorics: An International Journal
Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type

Journal of Algebraic Combinatorics: An International Journal
Flag-transitive symmetric 2-(96,20,4)-designs

Journal of Combinatorial Theory Series A
Reduction for primitive flag-transitive (v, k, 4)-symmetric designs

Designs, Codes and Cryptography

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Abstract

We present some results on flag-transitive symmetric designs. First we see what conditions are necessary for a symmetric design to admit an imprimitive, flag-transitive automorphism group. Then we move on to study the possibilities for a primitive, flag-transitive automorphism group, and prove that for λ ≤ 3, the group must be affine or almost simple, and finally we analyse the case in which a biplane admits a primitive, flag-transitive automorphism group of affine type.