Journal of the Australian Mathematical Society - Series A Vol. 64 Part 3 (1998) Application of the Bruhat-Tits tree of SU3(h) to some ${\tilde A}_2$ groups Donald I. Cartwright School of Mathematics and Statistics The University of Sydney NSW 2006 Australia and Tim Steger Istituto di Matematica e Fisica Università di Sassari via Vienna 2 07100 Sassari Italy Abstract: Let K be a nonarchimedean local field, let L be a separable quadratic extension of K, and let h denote a nondegenerate sesquilinear form on L3. The Bruhat-Tits building associated with SU3(h) is a tree. This is applied to the study of certain groups acting simply transitively on vertices of the building associated with SL(3,F), $F=\Q_3$ or ${\Bbb F}_3((X))$. PDF file size: 118K © Copyright 1998, Australian Mathematical Society