Finite Laguerre near-planes of small orders
by
Gunter Steinke
Department of Mathematics and Statistics, University of Canterbury

Finite Laguerre near-planes of order n basically correspond to interpolating systems of rank 3 over an n-set. For n a power of a prime, the classical example of a Laguerre near-planes of order n is the collection of all polynomials of degree at most 2 over the Galois field GF(n). This particular example extends to a Laguerre plane of order n by adding certain points at infinity.

In this talk we look at Laguerre near-planes of order n <= 7 from a geometric point of view and completely classify these planes. For n =/= 4 such a plane uniquely extends to a Laguerre plane. We further show that there are Laguerre near-planes of order 4 that do not extend to Laguerre planes and determine the automorphism groups of these planes and give characterisations of some of the planes in terms of their automorphism groups.

Date received: April 19, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacc-14.