
doi: 10.1007/bf02851105
A translation plane of order \(q^ 2\) is said to be 'likeable' when it has kern \(GF(q)\) and when its linear translation complement contains a group of order \(q^ 2\) whose elation subgroup consists of elements, which, when the plane is constructed from a spread in \(PG(3,q)\), fix a regulus. Such planes are studied in this paper, mostly in terms of \(4\times 4\) triangular matrices giving spreads, and are found, with exceptions, to belong either to a class of planes of odd order for which \(q\equiv -1(mod 6)\) previously studied by \textit{M. Walker} [''On translation planes and their collineation groups'', Thesis, Univ. London (1973)] or to a class of planes of even order for which \(q\equiv 2(\bmod 3)\) previously studied by \textit{D. Betten} [Geom. Deidcata 2, 327-339 (1973; Zbl 0272.50028)]. The proofreading for this paper was below standard. In particular the rows in the matrix in (2.3) have been transposed.
Kantor's construction, regulus, Translation planes and spreads in linear incidence geometry, Finite affine and projective planes (geometric aspects), spread, kern, collineation groups
Kantor's construction, regulus, Translation planes and spreads in linear incidence geometry, Finite affine and projective planes (geometric aspects), spread, kern, collineation groups
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