The norm of a Ree group

TL;DR

This paper explicitly constructs Ree groups of type G2 acting on Moufang hexagons, proves their fundamental properties, and shows that their norm is anisotropic, enhancing understanding of their algebraic structure.

Contribution

It provides an explicit construction and detailed proofs of properties of Ree groups of type G2, including the anisotropic nature of their norm.

Findings

Ree groups of type G2 are constructed explicitly.

The basic properties of Ree groups are established.

The norm of a Ree group is proven to be anisotropic.

Abstract

We give an explicit construction of the Ree groups of type $G_2$ as groups acting on mixed Moufang hexagons together with detailed proofs of the basic properties of these groups contained in the two fundamental papers of Tits on this subject. We also give a short proof that the norm of a Ree group is anisotropic.