Geodesic
A parametrisation for symmetric designs admitting a flag-transitive, point-primitive automorphism group with a product action
Ars Mathematica Contemporanea, Tome 23 (2023) no. 2, article no. 04, 14 p.

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We study (v,k,λ)-symmetric designs having a flag-transitive, point-primitive automorphism group, with v = m2 and (k,λ) = t > 1, and prove that if D is such a design with m even admitting a flag-transitive, point-primitive automorphism group G, then either:D is a design with parameters ((2t+s−1)2, (2t2 − (2−s)t)/s, (t2 − t)/s2)) with s ≥ 1 odd, orG does not have a non-trivial product action.We observe that the parameters in (1), when s = 1, correspond to Menon designs.We also prove that if D is a (v,k,λ)-symmetric design with a flag-transitive, point-primitive automorphism group of product action type with v = ml and l ≥ 2 then the complement of D does not admit a flag-transitive automorphism group.
DOI : 10.26493/1855-3974.2507.a1d
Keywords: Symmetric-designs, flag-transitivity, primitive groups, automorphism groups of designs 
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Eugenia O'Reilly-Regueiro; José Emanuel Rodríguez-Fitta. A parametrisation for symmetric designs admitting a flag-transitive, point-primitive automorphism group with a product action. Ars Mathematica Contemporanea, Tome 23 (2023) no. 2, article  no. 04, 14 p. doi : 10.26493/1855-3974.2507.a1d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2507.a1d/

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