AGANT SEMINAR
(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.