Abstract
Let q be a power of 2 greater than 2 and consider the group G = PSL2(q). We choose the maximal subgroups of G isomorphic to the dihedral groups D2(q+1) and D2(q-1) and present the primitive action of G on the right cosets of these two subgroups. We will find the orbits of the point stabilizer in each case and in the case of D2(q-1) we will prove there is an orbit Δ of the point stabilizer Gω, such that Δ ≠ {ω } and whose orbiting under G gives a 1-design with the automorphism group isomorphic to the symmetric group \( \mathbb{S}_{q+1}.\)
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Communicated by J.D. Key
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Darafsheh, M.R. Designs from the Group PSL2(q), q Even. Des Codes Crypt 39, 311–316 (2006). https://doi.org/10.1007/s10623-005-4926-3
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DOI: https://doi.org/10.1007/s10623-005-4926-3