Abstract
Given a finite group G, for all sufficiently large d and for each q > 3 there are symmetric designs and affine designs having the same parameters as PG(d, q) and AG(d, q), respectively, and having full automorphism group isomorphic to G.
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Kantor, W.M. Automorphisms and Isomorphisms of Symmetric and Affine Designs. Journal of Algebraic Combinatorics 3, 307–338 (1994). https://doi.org/10.1023/A:1022416002358
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DOI: https://doi.org/10.1023/A:1022416002358