On Flag‐Transitive Symmetric Designs of Affine Type | Zendy

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On Flag‐Transitive Symmetric Designs of Affine Type

Author(s) -

Biliotti Mauro,

Montinaro Alessandro

Publication year - 2017

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.21533

Subject(s) - mathematics , flag (linear algebra) , combinatorics , transitive relation , affine transformation , primitive permutation group , type (biology) , automorphism group , automorphism , block (permutation group theory) , prime (order theory) , symmetric group , discrete mathematics , pure mathematics , algebra over a field , cyclic permutation , ecology , biology

It is shown that, if D is a nontrivial 2‐ ( v , k , λ ) symmetric design, with ( k , λ ) = 1 , admitting a flag‐transitive automorphism group G of affine type, then v = p d , p an odd prime, and G is a point‐primitive, block‐primitive subgroup of A Γ L 1 ( p d ) . Moreover, O ( G ) acts flag‐transitively, point‐primitively on D , and D is isomorphic to the development of a difference set whose parameters and structure are also provided.

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