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Matrix spread sets of \(p\)-primitive semifield planes. (English) Zbl 0885.51008
Finite \(p\)-primitive semifield planes are constructed and classified for \(p\in\{3,5,7,11\}\). All these planes are of order \(p^4\) with kernel GF\((q^2)\). The task is carried out by finding all suitable spreads with a computer, and then checking for isomorphic ones. Well-known classes of semifields, such as Hughes-Kleinfeld and Dickson, are identified.

MSC:
51E15 Finite affine and projective planes (geometric aspects)
51A40 Translation planes and spreads in linear incidence geometry
12K10 Semifields
05B25 Combinatorial aspects of finite geometries
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