Classification of certain cotriangular spaces
by
Jonathan I. Hall
Michigan State University

Nearly thirty years ago Ernie Shult classified all finite graphs with the cotriangle property. The first step reduces the problem to the classification of certain finite partial linear spaces of order 2. In particular the class of all cotriangular spaces (reduced or not, finite or not) is seen to be the class of all partial linear spaces in which each plane is a Latin square design. The classification up to isomorphism of all cotriangular spaces follows Shult's model. Every cotriangular space has a canonical reduced image, and all such have been classified. In the non-reduced case the extension problem can be difficult. A definitive solution is only known when each planar Latin square design comes from the multiplication table of a group of order 2, a step in the classification of 3-transposition groups. We discuss the more general situation where planes are Latin square designs coming from cyclic groups of arbitrary order.

Date received: March 10, 2001

Copyright © 2001 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 # cagg-19.