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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
##### Keywords:
$$p$$-primitive semifield planes
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