Abstract
In 1965 Knuth showed that from a given finite semifield one can construct further semifields manipulating the corresponding cubical array, and obtain in total six semifields from the given one. In the case of a rank two commutative semifield (the semifields corresponding to a semifield flock) these semifields have been investigated by Ball and Brown (2004), providing a geometric connection between these six semifields and it was shown that they give at most three non-isotopic semifields. However, there is another set of three semifields arising in a different way from a semifield flock, hence in total six semifields arise from a rank two commutative semifield. In this article we give a geometrical link between these two sets of three semifields.
Citation
Michel Lavrauw. "The two sets of three semifields associated with a semifield flock." Innov. Incidence Geom. 2 101 - 107, 2005. https://doi.org/10.2140/iig.2005.2.101
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