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Abstract
This paper is devoted to the classification of flagtransitive 2(v,k,2) designs. We show that apart from two known symmetric 2(16,6,2) designs, every flagtransitive subgroup G of the automorphism group of a nontrivial 2(v,k,2) design is primitive of affine or almost simple type. Moreover, we classify the 2(v,k,2) designs admitting a flag transitive almost simple group G with socle PSL(n,q) for some n≥3. Alongside this analysis we give a construction for a flagtransitive 2(v,k−1,k−2) design from a given flagtransitive 2(v,k,1) design which induces a 2transitive action on a line. Taking the design of points and lines of the projective space PG(n−1,3) as input to this construction yields a Gflagtransitive 2(v,3,2) design where G has socle PSL(n,3) and v=(3^{n}−1)/2. Apart from these designs, our classification yields exactly one other example, namely the complement of the Fano plane.
Original language  English 

Article number  105309 
Journal  Journal of Combinatorial Theory. Series A 
Volume  177 
DOIs  
Publication status  Published  Jan 2021 
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 1 Public lecture, debate or seminar

Combinatorial designs and symmetry
Alice Devillers (Speaker)
26 Feb 2021Activity: Service and engagement › Public lecture, debate or seminar