
doi: 10.1007/bf01265323
Let \({\mathcal T}\) be a translation plane of even order \(q\) with translation line \(I_ \infty\). An oval \({\mathcal O}\) in \({\mathcal T}\) is called a translation oval if \(I_ \infty\) is a tangent at a point \(a\) and if the stabilizer of \({\mathcal O}\) in the translation group acts transitively on \({\mathcal O}\setminus\{a\}\). An \(i\)-pencil (\(0\leq i\leq 2\)) is a collection of \(i\) lines and \(q+1-i\) translation ovals through a point \(u\) which partition the set of points different from \(u\) which are not in \(I_ \infty\). Pencils in \({\mathcal T}\) can be used to construct new translation planes since pencils correspond to certain spreads. The authors characterize 2-pencils in \(\text{PG} (2,q)\) and describe certain group transitive 1-pencils. The authors leave the investigation of 0-pencils to a forthcoming paper.
spreads, Translation planes and spreads in linear incidence geometry, translation plane, Finite affine and projective planes (geometric aspects), ovals
spreads, Translation planes and spreads in linear incidence geometry, translation plane, Finite affine and projective planes (geometric aspects), ovals
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