Narrow Results

We give a short and elementary proof of the fact that a finite special Moufang set with root groups of even order is isomorphic to the unique Moufang set whose little projective group is PSL₂(2^k) for some integer k ≥ 1.

In this paper we classify finite special Moufang sets 𝕄(U,τ) of odd characteristic. The characteristic 2 case was handled in another paper by De Medts and the author (see [3]). We prove that U is elementary abelian. Then, we show that 𝕄(U,τ) is the unique Moufang set whose little projective group is PSL₂(|U|). The emphasis of this paper is on obtaining elementary proofs. Section 3 deals with root subgroups in any Moufang set and may be of independent interest.