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On some new classes of semifield planes. (English) Zbl 0812.51002
It was shown by Y. Hiramine, M. Matsumoto and T. Oyama [Osaka J. Math. 24, 123-137 (1987; Zbl 0646.51006)] that with every translation plane of order $$q^ 2$$ whose kernel contains $$GF(q)$$ one can associate a translation plane of order $$q^ 4$$ whose kernel contains $$GF(q^ 2)$$. The authors investigate the semifield planes obtained by this construction. It turns out that in most cases these planes do not belong to a known class of semifield planes.

##### MSC:
 51A40 Translation planes and spreads in linear incidence geometry 51E15 Finite affine and projective planes (geometric aspects) 12K10 Semifields
##### Keywords:
translation plane; semifield planes