Characterizations by automorphism groups of some rank 3 buildings, III. Moufang-like conditions

Abstract

In this paper, we introduce the root-Moufang condition and the p-adic Moufang condition. We show that affine buildings of type A2 satisfying the root-Moufang condition are Bruhat–Tits buildings. Also, every rank 3 affine building satisfying the p-adic Moufang condition is a Bruhat-Tits building. We motivate the introduction of the new conditions by showing that all Bruhat– Tits A2-buildings satisfy the root-Moufang condition, and that the A2-buildings over a p-adic field also satisfy the p-adic Moufang condition. Another application of the p-adic Moufang condition is given in Part IV of this paper.