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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.