(Algebraic Geometry, Algebra and Number Theory Seminar)

Date/Time/Room: Thursday, Oct 24, 2002, at 12:30 pm in 487 Pickard Hall

Speaker: Minerva Cordero, Department of Mathematics, UTA

``On the Semifield Planes of Order 54 and Kernel GF(52)''

Abstract: A semifield is a non-associative division ring. To every semifield S, we associate an affine plane with points the ordered pairs (a, b), where a, b in S. The left nucleus (kernel) of S is the set of all elements s in S such that s(a.b)=(s.a)b for every a, b in S. The order of a semifield is the number of points in a line. In this talk, we study the semifields of order 54 and kernel GF(52). We show that there are 13 non-isomorphic semifield planes of order 54 and kernel GF(52); one is the Desarguesian plane coordinatized by GF(54), three are coordinatized by the Generalized Twisted Fields of Albert and 9 are p-primitive planes.