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Dual parallelisms


Abstract


Assume that \rho is a parallelism in PG(3,K), for K a field, that admits a collineation group G that fixes one spread \Sigma and acts transitively on the remaining spreads of \rho. If G contains suitable central collineations of \Sigma then it is shown that the dual parallelism is a parallelism that can never be isomorphic to the original. The results show that the Johnson parallelisms of Hall or Knuth type, the Johnson-Pomareda parallelisms of type f and all of the "derived" parallelisms produce dual parallelisms which are parallelisms but are nonisomorphic to the original parallelism.

DOI Code: 10.1285/i15900932v21n1p137

Keywords: Parallelisms; Dual parallelisms

Classification: 51E23; 51A40

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