\(m\)-parallelisms
In [\textit{N. L. Johnson}, `Subplane covered nets', Pure and Applied Mathematics, vol. 222, Marcel Dekker, New York (2000; Zbl 0954.51002)] a group-theoretic construction of a class of parallelisms in \(PG(3,K)\), \(K\) a field admitting a quadratic extension, is given. Such parallelisms enjoy the property that there exist a unique Pappian spread \(\Sigma_1\) and a collineation group \(G\) of the parallelism, which is also the full central collineation group of \(\Sigma_1\) with fixed axis \(\ell\). Also \(G\) is transitive on the remaining spreads of the parallelisms, and all spreads involved are Hall spreads. Here the authors give a generalization of the above construction, using the full central collineation group \(G\) of an associated Pappian spread, choosing \(m\) Pappian spreads instead of a second Pappian spread, sharing a regulus with the original Pappian spread. They construct this way many parallelisms.
scientific article; zbMATH DE number 1852878