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- W2022952011 abstract "Let oxy denote a fixed autotopism triangle of a finite commutative semifield plane of even order qN, with middle nucleus GF(q). A point I ∉ {x, y, o} is called a central unit of the plane, relative to oxy, if coordinatising the plane by a semifield, in the standard way with I chosen as unit point and ox, oy as axes, yields a commutative semifield DI. It is shown that the set of all central units, relative to a fixed oxy, is partitioned by a set of q − 1 translation (hyper)ovals, any two of which share only the origin o as a common point. The full autotopism group acts transitively on these q − 1 translation ovals, and the ovals, together with the lines ox and oy, define a rational Desarguesian net of degree q." @default.
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- W2022952011 date "1996-08-01" @default.
- W2022952011 modified "2023-09-24" @default.
- W2022952011 title "An oval partition of the central units of certain semifield planes" @default.
- W2022952011 cites W142223789 @default.
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- W2022952011 doi "https://doi.org/10.1016/0012-365x(94)00376-t" @default.
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