139 research outputs found
Parallelism
No full textEnProblems involving the idea of parallelism occur in finite geometry and in graph theory. This article addresses the question of constructing parallelisms with some degree of "symmetry". In particular, can we say anything on parallelisms admitting an automorphism group acting doubly transitively on "parallel classes"
Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 52, fasc. 1.
No full textAtti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 53, fasc. 1
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On 2-transitive 3-nets
No full textA 3-net is said to be 2-transitive if it admits a group of direction-preserving automorphisms fixing one of the transversal lines and acting 2-transitively on its points. We classify the 2-transitive finite 3-nets which do not admit a proper 2-transitive 3-subnet, except, possibly for a subnet of order 2. The result is then extended under a weaker assumption
Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 55
No full textEvery equidistant linear code is a sequence of dual Hamming codes
No full textIf an equidistant linear code exists, then its parameters must satisfy certain relations determined by the Plotkin bound. For each set of possible parameters there actually exists an equidistant linear code with these parameters: its generator matrix is a sequence of parity check matrices of Hamming codes. The generator matrix of every equidistant linear code can be brought to this form by suitably rearranging its columns
Point-primitive inversive planes of odd order
No full textThe following Theorem is proved. If I is a finite inversive plane of odd order n and G is an automorphism group of I acting primitively on its points, then I is miquelian; furthermore, we have PSL(2,n^2) <= G <= PGammaL(2,n^2) and G is 2-transitive on the points of I unless n=3 and A_5 <= G <= A_5 * C_
Atti del Seminario Matematico e Fisico dell'Università di Modena e Reggio Emilia, vol. 53, fasc. 2
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