On Flag‐Transitive Symmetric Designs of Affine Type |
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| Authors: | Mauro Biliotti Alessandro Montinaro |
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| Affiliation: | Dipartimento di Matematica e Fisica “E. De Giorgi,”, Università del Salento, Via per Arnesano, Lecce, Italy |
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| Abstract: | It is shown that, if  is a nontrivial 2‐ symmetric design, with  , admitting a flag‐transitive automorphism group G of affine type, then  , p an odd prime, and G is a point‐primitive, block‐primitive subgroup of  . Moreover,  acts flag‐transitively, point‐primitively on  , and  is isomorphic to the development of a difference set whose parameters and structure are also provided. |
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| Keywords: | Symmetric design difference set flag‐transitive affine group |
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is a nontrivial 2‐
symmetric design, with 
, admitting a flag‐transitive automorphism group G of affine type, then 
, p an odd prime, and G is a point‐primitive, block‐primitive subgroup of 
. Moreover, 
acts flag‐transitively, point‐primitively on 
, and 
is isomorphic to the development of a difference set whose parameters and structure are also provided.