A new construction of the Ree groups of type 2G2

We give a new elementary construction of Ree’s family of finite simple groups of type 2G2, which avoids the need for the machinery of Lie algebras and algebraic groups. We prove that the groups we construct are simple of order q3(q3 +1)(q − 1) and act doubly transitively on an explicit set of q3 +1 points, where q = 32k+1. Moreover, our construction is practical in the sense that generators for the groups and many of their maximal subgroups may be easily obtained