Vol. 2, No. 1, 2005

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The two sets of three semifields associated with a semifield flock

Michel Lavrauw

Vol. 2 (2005), No. 1, 101–107
DOI: 10.2140/iig.2005.2.101

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.

semifields, translation planes, finite geometry
Mathematical Subject Classification 2000
Primary: 12K10, 51E15
Received: 23 September 2005
Accepted: 21 October 2005
Michel Lavrauw