Half-isomorphisms of finite automorphic Moufang loops
  We show that each half-automorphism of a finite automorphic Moufang loop is trivial. In general this is not true for finite left automorphic Moufang loops and for finite automorphic loops. 
A. Grishkov, M.L.Merlini Giuliani, M. Rasskazova, and L. Sabinina
math.GR