On Some Automorphisms of Orthogonal Groups in Odd Characteristic

Abstract

In this paper, it is proved that the simple orthogonal groups O 2n+1(q) and O 2n ± (q) (where q is odd) cannot be automorphism groups of finite left distributive quasigroups. This is a particular case of the conjecture stating that the automorphism group of a left distributive quasigroup is solvable. To complete the proof of the conjecture, one must test all finite groups.